1995 Geo Prizm Car won't start/turn over

Lately when I have been putting my car in reverse, just after starting it, it seems like it is going to stall. Today it did stall, and now will not start again. When I turn the key, the electric comes on, and the engine chugs, but it does not turn over all the way, and the car will not start. It has been very cold in Michigan lately, and I have only noticed the problem of my car almost stalling when I first start it up. Today it did stall for the first time, after putting it from park into reverse, and now is not starting again. When I turn the key, the electric comes on, and the engine turns over as long as I keep the key turned all the way, trying to start the car, but the engine never completely catches/turns over, and the car doesn't start. Any idea what might be wrong, or any cheap remedies I can try?