iPhone 3gs died won't turn on when connected.

My iPhone 3gs was staring to get a bit slow so I decided to restore it to see if that helped, it's only made things worse though.

I left it on the dash of my car since the restore and it's blacked out twice now. I can only get it back on by plugging it into my Mac. I can't hold down the on and main buttons together as the on button has packed in.

I thought that it might be becasue the iPhone is overheating so I had a look at the logs. I can see this a lot but not sure if it's the problem.
Which doesn't exactly sound promising, but I don't think that it is overheating leading to the problem.

Today however, I was browsing on Safari, the screen flicked and then the iPhone died. I can't even get it to come back on by plugging it it.

Any suggestions?

I would paste more logs but I can't seem to find the important ones anymore. I did notice this line in the logs from todays activity before I lost them.

Hmmm good and bad news now.

The phone was one when it 'died' but the screen was blank. I think that 0x8badf00d means that it got stuck in an infinite loop.

This sounds right as the battery died and I managed to get the iPhone back on when connected to my computer. I tried a restore and now this is what I'm getting.

iPhone 3gs Restore - YouTube

It looks like an old ZX Spectrum trying to load!

It's flicking between that and a normal restore screen but the bar wont move.

Are there any log files that I can post up to help diagnose the problem?