Why can't I see anything in the viewfinder or via Live View when my camera is connected to my telescope?

You will need to refocus after removing the eyepiece and placing the T-mount adapter and camera directly on the telescope's focusing tube. When it's severely out of focus you will not see anything because the light from any stars in the field will be spread too thin.

One way to get a new combination of pieces in the ballpark quickly is to use the moon as a target. It's large enough and bright enough that even when out of focus something can be seen through the camera's viewfinder or on the LCD when in Live View. Then rack the focus in and out until you find the point of focus.

Since your telescope is a Newtonian reflector, the optical distance from the camera's sensor to the primary mirror should be the same as the telescope's focal length. If you can measure the distance from the center of the mirror to the center of the secondary mirror, subtract that from the telescope's focal length of 1,000mm. The difference is how far the camera's sensor, which is 44mm behind the camera's lens flange, should be from the center of the secondary mirror.

Telescope optical design

This is a Bird Jones telescope (more on that in a moment). Regardless, both Newtonians and Bird-Jones designs have a common issue that often prevents them from being used with many cameras.

To understand the problem it is important to recognize just what "focal length" actually means. In simple terms, if a telescope has a 1000mm focal length, then it means that the instrument will bring an image to focus 1000mm AFTER light begins to focus. On a Newtonian design telescope, this is the surface of the primary mirror. Here's a diagram from Wikipedia:

Note that in this diagram, the light enters from the left ... but does not start to focus until it reflects off the primary mirror at the right. This is a parabolic mirror which focuses light at some distance away based on the focal length of the telescope. E.g. if it were a 1000mm focal length, then the image will come to focus 1000mm away.

In this diagram, that point would be the gray X at the far left ... except that light will hit the secondary mirror (a flat mirror set on a 45° angle) to bounce the light out to the side of the telescope where it reaches the 1000mm distance at the red X (instead of the gray X).

Prime Focus

When you insert an eyepiece (I'll address camera issues in a moment), the point of the focuser is to move the eyepiece to that focus point. Eyepieces usually are not "parfocal" with other eyepieces. "Parfocal" means that if you remove one eyepiece and insert another, the telescope will still be accurately focused. Some eyepiece vendors make specific eyepiece sets designed to be parfocal -- but most are not. This means it is necessary to re-focus the instrument each time you change eyepieces.

Bird-Jones Telescopes

The Celestron 114LCM is a "Bird Jones" design telescope. These are telescopes that resemble Newtonian reflectors ... but have a few key differences.

Among the differences are

1. It uses a spherical primary mirror (a Newtonian uses a parabolic primary mirror). This will result in spherical aberration.
2. Their physical length is typically about half their focal length.
3. They use a builtin barlow (which may double as a spherical aberration corrector) to compensate for the physical focal-length shortage.

This means the optical path is closer to 500mm long (for a 1000mm telescope) and that there is a built-in 2x barlow at the base of the focuser on the side of the telescope.

The "Bird Jones" design is used mostly as a cost-savings technique to allow for cheaper manufacturing costs. It is much easier to mass produce a spherical mirror than it is to produce a parabolic mirror (where the curvature is constantly varying across the surface). But this creates a spherical aberration problem and this requires additional optical components to act as a corrector. Usually, however, the "corrector" is a simple 2x barlow which uses the increase in focal length and focal ratio as a means to reduce the aberration effects.

The manufacturer will sometimes claim the scope is a Newtonian reflector (The Bird-Jones is a derivative of the Newtonian, but is not a true Newtonian.) The manufacturer is able to produce significantly cheaper mirrors (one of the major expenses) and cut the physical length of the instrument by half (since it is using a 2x barlow).

Experienced astronomers usually discourage new telescope buyers from selecting these instruments.

Here's an article in Sky & Telescope on what telescopes to avoid: HOBBY KILLERS: WHAT TELESCOPES NOT TO BUY. There is one particular paragraph worth emphasizing:

There’s one design you should avoid at all costs: the “Bird-Jones” reflector. The Bird-Jones design uses a spherical primary, and a fast one at that, in an attempt to keep the tube shorter than average. Manufacturers of this design correct for spherical aberration and increase the focal length by placing a corrector lens at the inner end of the focuser. The corrector lens is supposed to make everything all right again, but it never does. The view through every Bird-Jones scope I’ve ever looked through has been uniformly awful. There might be a decent Bird-Jones telescope somewhere out there, but if there is, I’ve never seen nor even heard of it.

That's not great news for you since you already have your telescope. But the reason I wanted to share this (bad news, such as it is) is to emphasize: The issues you are likely to have with this instrument are not necessarily your fault. Another instrument is likely to provide a better experience.

If you are interested in astrophotography, my first suggestion is to learn the night sky and become well acquainted with use of your astronomy gear before attempting to image through it. But also, start with short focal-length equipment. High focal-length telescopes require use of auto-guiding and that really complicates things. I would also suggest that 2/3rds of the budget for astrophotography gear should be spent on ... the telescope mount (surprise!). A bad mount will ruin every photo regardless of how excellent the telescope might be otherwise. But a short focal-length (e.g. around 500mm) can be very forgiving and that makes things less frustrating when starting out.

Focus with a DSLR camera

In order to focus with a camera (any camera) the focal plane must be moved to the focus position (the red X in the diagram). This might seem trivial, but there is a complication with DSLR camera bodies. The camera uses a reflex mirror positioned in front of the sensor. But this means it needs room for the mirror. On a Canon EOS DLSR that uses either EF or EF-S lenses the distance from the lens mounting flange on the front of the body to the imaging sensor is 44mm.

To mount such a camera on a telescope, a prime-focus nose-piece is needed. This is a simple tube having the same diameter as a telescope eyepiece (either 1.25" or 2" diameter barrel) and an adapter that has the camera's bayonet mount so it can attach to the camera body. The mount probably adds about 5mm to the overall focus distance.

This means the total distance from the mount to the imaging sensor is about 49mm (roughly 2").

The issue with the telescope is that even if you rack the focus all the way "in" it still isn't able to bring the imaging sensor to the focus position.

Newtonian Astrograph Telescopes

There is a variant of the Newtonian telescope where the primary mirror is shimmed forward roughly 50mm (about 2") and uses a slightly larger secondary mirror. This moves the focus position about 2" farther away from the optical tube... enough so that the image sensor on a DSLR camera can be positioned precisely at the focus position.

Refractor telescopes and Schmidt Cassegrain Telescopes (SCT's) put the eyepiece at the rear of the telescope. This makes it more difficult to look through because an observer needs to get low and look "up" into the eyepiece (a ticket to back-pain and a visit to the chiropractor). To resolve this, those telescopes add a diagonal at the rear of the scope so you can look "down" into the scope. But this diagonal also adds a couple of inches to the focus path and the telescope is designed to take this into account. To use a DSLR camera on one of these scopes, just remove the diagonal (subtracting about 2" from the focus distance) and then attach the camera (adding about 2" to the focus distance) and you've "balanced the books" ... now the telecope is able to come to perfect focus.

Other cameras

Another option is to use cameras that don't need a reflex mirror. This allows the imaging sensor to be positioned toward the front of the camera -- usually less than 20-25mm flange-to-focal-plane distance. The advantage here is that the focuser usually will have enough travel to compensate for the sensor position.