Temporary loss of power

I have a 1992 Chevy Cavalier with around 79,000 miles on it. Background info: the car was previously owned by a man who drove the car only 3000 miles over the last 7 years and then hit a small tree dead center in the front end of the car, causing the hood to be slightly raised, but it still latches properly. It kind of looks like it's popped all the time, due to the wrinkles that have formed from wind or whatever getting under it.
First problem was a dinging noise, like a reminder noise if you leave your lights on, that only happens when it rains or snows. It will ding until the car comes to a complete stop, then it will stop. Sometimes it will start again, stopping again when the car stops again. Annoying. But then the horn stopped working, and there is not a burnt out fuse. Then, since it has started snowing, sometimes when I start the car after it has been sitting for a long time, it will immediately stall and all the presets on my radio are lost, like the battery is dead. But then it will start right up and act fine, until the next time I go to start it. I have checked the connection of the cables to the battery, and they are tight. I don't know that these things are related, but I am most concerned about the seeming battery problem.
Could it be due to the moisture getting under the hood? If so, short of getting a new hood and the dent pulled out, what could I do?
Thanks.