Alright folks, here's what I've got:
An S3, which is rooted, using TWRP for recovery and was on a CM11 nightly. This had been running happily with no problems since February. It was stock up until that point, when the OTA update to 4.3 caused major issues.
About a week ago, it began randomly shutting down / restarting.
Two days ago, it did this again while I was surfing the internet, but then proceeded into a boot loop and now will not start up at all. It shows the Samsung screen, then the Galaxy S3 screen, then stops and loops on the CM animated screen. As far as I know I didn't do anything to trigger this - no new app downloads, no new ROM flashing, etc - it just did it suddenly in use.
I can successfully get into both download mode and recovery and the phone will stay there (so I don't think this is the power button issue), but I can't do anything from either mode. In TWRP I get error messages regarding failure to mount cache regardless of what I do. I can't do a factory reset or wipe it. If I try to format, it will hang forever.
In Odin anything I have tried comes up "Fail", or "Complete - Write Operation Failed". Can't flash back to stock, can't flash CM again. I've tried a couple different cables and different USB ports, and reinstalling the drivers. The computer in question, which has worked with Odin before, is running Win 8.
I'm at the end of what I know to do to this thing, and beginning to suspect it has a hardware problem. Any thoughts or things to try?