Car not starting after week of sitting in cold temperatures

Three weeks ago I bought an ’03 Honda Civic. It’s been running well so far, but I let it sit outside without using it for a week and a half in 10 to -10 F temperatures. After this, the car wouldn’t work at all (no lights on the dash, no attempt to turn over, no security system… absolutely nothing).

I figured the battery probably froze, so I brought it in to get it warm again (It didn’t look like it was buldging at the sides too much). Now I’ve put the battery back in and the dashboard lights work again. However, the security system still doesn’t work (ie it doesn’t lock with my fob — I have to do it by hand) and the car won’t start. When I turn the key all the way, it makes one attempt to turn over but then the lights just flicker on and off quickly, and it doesn’t start. Is my battery completely shot, or is it just low on charge? Or is it something else entirely?

I plan on asking a friend to help jumpstart my car in the next few days. If it doesn’t work might that be a sign the alternator is shot?

Here’s some additional information that may be of use:

— The previous owners had become disabled and therefore had no use for it, so it might have been sitting for a while in their possession too. Though in general it looks like they took good care of it.

— I made a mistake by putting on the ground second instead of first when reattaching the battery, and there were some sparks. Could this possibly have shorted the system?

–I noticed that there is no antifreeze in the clear overflow container. Though the radiator is full.

— When I removed the battery, one of the bolts on the battery terminal broke. I bought a new bolt and nut at the hardware store and used that. I didn’t buy any special kind — just regular bolts and nuts. Do you need a special kind for this part of the car?