Cannot boot phone, just hard shuts off topic

I've had issues with this phone where if I take it off of the charger, It'll just completely turn off.
Sometimes also just with random usage even on charger
Now, its not even booting up, it'll hit the AT&T boot splash and immediately turn off.
Before that it would finish the AT&T boot splash and then turn off.

Recovery mode works fine, so does Download mode.
I've used the Heimdall One-Click program and while it runs fine, doesn't help.

It's running Gingerbread iirc.
EDIT: Also battery charges up just fine, and yes I've searched around the forums.