3GS randomly rebooting / now stuck in restore mode with error 29
Preface: I have browsed similar topics but haven't seen this combination asked yet (although I am willing to admit defeat if it has been asked).
About 3 weeks ago my iPhone 3GS 16GB began randomly rebooting itself in 10-20 minute intervals. Superficial research led me to believe it was an issue with iOS 4.3.x and the 3GS, so I attempted to downgrade to 3.1.3. I wasn't able to downgrade successfully (error 3196), so I just kind of lived with the rebooting issue for a few days.
Within 4 or 5 days, the issue seemed to resolve itself. Phone behaved fine for about a week.
Waking up one morning, I tried waking up my phone (which was still connected to the AC adapter) and nothing happened. Completely dead. Couldn't power on, couldn't get into DFU mode, nada. Later on, I tried charging it again, and noticed the screen was actually flickering black (like the apple logo screen, without the apple). While charging, pressing and holding the home and power buttons somehow caused it to boot.
Now I am stuck at the iTunes screen (iTunes logo and USB cord). iTunes recognizes my phone (Device Manager recognizes Apple USB drivers) and wants to restore and update to iOS 4.3.5. Everytime I go through this process, the restore fails around "updating firmware", giving Error 29. It should be noted that I've tried restoring from multiple computers, with multiple completely new installs of iTunes and QuickTime.
Is this a battery issue? Should I try ordering the kit and seeing how it goes? I don't know what APN is in my phone currently. I've had the phone for about a year and 4 months, with no issues prior to this.
Any feedback would be greatly appreciated!