I'm not 100% sure this is the case, but failed internal memory issue happens to Captivate phones and the symptoms are same to what you describe. The phone can't read part of the memory and reboots constantly no matter what ROM you attempt to flash. Search the forum for internal/external swap methods. I never had to deal with this issue and have no experience with workarounds.
- HTC Desire 601 LTE, KK Android 4.4.2 (main phone)
- Acer Iconia Tab A200, ICS Android 4.0.3 (games tablet)
- Samsung i896 Captivate, JB Android 4.2.2 (backup phone)