Iphone 4 Shuts off at 55% and above (I.O.S 7.0.4)

I recently have been having troubles with my iPhone 4.

I replaced the screen about 4 weeks ago with no issues. Then the battery started acting up about a week later. It wouldn't charge past 45% and would die all the time even when plugged in. Then I figured maybe the battery just happen to die too. The phone is about 13 months old. I replaced the battery and it worked for about 2 days. It would charge up to 100% and work fine until about 76% then it would start to act up again (shutting down on its own) It does this also sometimes around 90%. Once it gets down to about 55% it turns on when i turn it on. But it turns right back off once it is on for about 5 seconds.

I would like to think it is a battery calibration issue with the new battery because it will not turn off when it is plugged in (unlike the old battery which would turn off even when plugged in!) and it functions normally and still charges to 100%.

I do not know how to accomplish calibration though because it turns off right away at 55% so I can't seem to get lower than that.

I let it discharge to 55% and recharged it back to 100% and it seems to be working fine now, (only restarted once) but i fear it will start acting up again around 75ish%

Any help would be greatly appreciated.

I also checked the diagnostics and usage and it always says something like reset counter then in there it says boot fault vdd_under and boot stage 255 or 80

if that helps at all.

Thanks again,

Collin