How to fix iPhone not recognized?

Okay. I have an iPhone 4 32Gb running 4.3.3. I bought this phone recently off craigslist. I can't get it to be recognized on any computer or sync. I want to restore it because it has some problems, in the software, I believe. The battery won't charge all the way even after a full night and it also dies after a day of school even if I'm not using it. It also heats up tremendously. I don't believe it is the hardware. Also, I just bought a brand new battery. I have tried everything to fix it though. Multiple cables, different computers, restore mode, dfu mode, new charging ribbon. I have also tried Reinstalling itunes various times on two computers and Restarting Apple's Mobile Device Support. Could a new iphone cable work? I only have ones from my ipod touch 3g. Also, what about a MAC computer instead of PC? Please Help.

I also forgot to mention, It charges when I plug it in. I just get Code error 43 from my PC.