Replaced Charge Port and Battery, will only charge once battery is dea

I have acquired a water damaged (washing machine) iPhone 4. The original owner said she could not get it to charge at all. Just out of curiosity, I plugged in the charging cord and...Voila, it began charging. After a full charge, I thought "Sweet!" I've got an iPhone that I'll keep and use as an iPod. With the exception of activated the cellular service on the device, everything seemed to be working just fine. I updated the operating system to iOS 7 and downloaded a few apps and music. Again, the intention was just to use it as an iPod.

With the battery down to about 40%, I tried to charge it again. This time...nothing. I tried several different charging cords...nada. I immediately thought the problem was with the charge port flex but replacing it didn't work. Thinking it was no use, I put it aside for a while. A couple of weeks later, once the battery was dead, I tried charging it again. And, just like before, it charged completely and functioned fine excepted when I tried to charge it again with about 80% charge.

This time I thought maybe the battery itself was the culprit, I tried two different (brand new) batteries. Still having the same problem. I have tried several soft resets which have not worked. Also, my computer will not detect it when connected.

Any ideas?