iPhone 4 broken due to software problem

Hi, last year my iPhone 4 started acting up until one point where it wouldn't boot up past the Apple logo. I brought it to be repaired (not from apple directly), but they couldn't as it lost some sort of ID number that meant it was dead for good (sorry, can't be more specific on what was missing exactly, I forget what it was called).

Anyway, I've been reading around and am being lead to believe there's still hope for it. The guy who repaired it said the internals were perfect, just that it was missing some software identification code -he said Apple removes them at times to get people to upgrade -bit too much of a conspiracy for me to fully believe.

So what do you think might be wrong with it, and is there any chance of repairing it at all?

 

Nobody has any idea what's gone wrong here, do they?

 

I just decided to charge it and it actually booted up in iOS 7, even though I never updated it to that before. Anyway, it's charging very, very slowly, like 8% in 7 hours.

It wants to connect to iTunes, but upon doing that iTunes says there's a problem with it.

I don't know what. I know the 30 pin connector, battery and wifi chip could do with changing, but I'm not sure what else could be wrong with it.

Any ideas?