Unhappy [Q] AT&T HTC One X+ Battery instant drain & turn off

I recently bought a used HTC One X+ which was pretty messed up by the previous owner, and through pure luck I eventually managed to get it re-flashed to an upgraded stock 4.2.2.

Since I got it I have been having very weird battery issues. I would charge it to 100% and it would seem to keep most of the charge for a long time, slowly draining which was great I thought. Then all of a sudden it would just turn off at something, like 70%, and when I went to turn it back on I would discover that the battery was completely drained to 0% instantly, I tried some apps that claim to fix battery issues, but they didn't work. I am stating to think the battery is defective and needs to be replaced. If not, is there a soft fix for this?

I read about moving a file from system/bin to system/app but when I reboot into recovery and go to the file manager the system/bin is empty and there is no system/app folder.

The phone boot loader is unlocked and the phone is rooted.

Solutions will be appreciated.