Why is my Nikon D3300 taking almost totally black pictures through the viewfinder but is fine on liveview?

Try this. Remove the battery. If you have a new fully charged battery insert it. If not, try fully recharging your battery before reinserting it into the camera. Next, turn on the camera and press the LIVE View button and see if you can see through the View Finder and see a clear image. Also, Do you hear a mechanical switching noise of the mirror when you press on the LIVE View button?

Looks like the mirror may not be swinging out of the way correctly when the shutter fires. Try this :

Put the camera on viewfinder mode, put it to your eye and take a picture. The viewfinder image should go dark for a fraction of a second as the mirror swings out of the way and returns.

If it does, there could still be an issue with the synchronisation between the mirror and the shutter. Try a really long shutter time, say 1 second. If the mirror swing is just slightly delayed, you'll probably get an image this time as the mirror gets out of the way part way through the exposure. If it's gone really bonkers, the mirror might not move until the shutter closes, in which case the viewfinder won't go dark until after the exposure is complete.