I had similar problems with an Old Acer 5100 (a friend's) and sent it back under warranty twice with no help.
I found that (this is really simple but worked quite well) his CPU was overheating due to an excess of dust in his fan, so much that it shut down often, was unstable and overheated (up to 95 (deg) c). Cleaning out the entire computer fixed the overheating problem and his DVD problem was a result of the drive not being fully hooked up. Acer warranty service was extremely unhelpful. You ship it to Texas and if it starts they send it right back saying there were no problems, great huh?
I'd try those two things, if it works let me know, if not let me know and I'll do some more research and check out those notebooks see if I can come up with a fix.
EDIT: as for the battery, you prob need a new one due to extreme heat of the computer. I'd recommend a 9 cell for extended battery life (up to 8 hrs).