To be honest, if it was destroyed in a car accident just about anything is possible.
Was it a bad accident, and do you know if the phone copped much of an impact, ie was it thrown across the car and slammed in to a door panel for example?
I can think of a few possibilities:
1. Damaged Battery
2. Damaged circuit board from the impact
3. 1 or more sensitive components damaged
4. An already suss solder joint losing connection
The battery is obviously easy enough to check (if you can borrow one)
If not the battery I would think it's most likely one of the other points I've raised, if this is the case it won't be easy (or cheap) to fix unless you have a mate experienced in this sort of thing.
If you even consider taking to the board with a soldering iron, make sure you use someone with experience. Not a job for beginners.
Cheers Paul