Restart issues, possibly hardware?

Okay so it seems only I get the weird electronics.

My iPhone 3gs was running smoothly until a couple of months ago. I was running apps and games and whatnots. But while i was reading a pdf file on quickoffice, it decided to restart itself on its own. This repeated for a while. Thinking it might be a software problem, I restored it.

Post this, it got to a point where it wouldn't even charge at all. Even if it did, it would shut off every three minutes or so. But only if used. If left alone, it would go on for the entire day. Anything above three minutes, and it restarts.

Also, how i got it to charge was to perform a hard reset every time i needed to charge the phone. It would then work okay for a while and start acting up again pretty soon.

Any help?? Please?

-Update-

So I've changed the battery, and it hasn't really solved the issue. The battery percentage stays stuck at a 100%. What do i do now?? And it still sometimes restarts on charging.