Welcome to Android Central! What do you mean by completely rebuilding the system? Do you mean that you simply did a factory reset, or did you actually re-flash the firmware?
This issue is not software problem, mostly comes from cracked battery connector. Remove the back cover, apply pressure on the battery connector would stop the problem, this battery connector must be re soldered to fix this issue.
Read this post for more information of Note and Tab Pro, two almost identical tablets with the same problem.
Factory reset cannot fix a hardware issue as you did.