iPhone 4 restarts every 3 min

Solution 1:

Did your iPhone was jailbroken before the color swap?

If so, I'm afraid you broke something inside the phone. Something the OS is trying to access and since it's broken, respring the springboard (maybe that's a bug, but since you're not supposed to fiddle with the inside of the phone, it's not something you could use to replace it).

As a last resort, you could try to reopen it and see if there's anything that looks broken.

Solution 2:

In my case it was the battery. I got a friend to lend me his iPhone and after switching the batteries, the problem was gone. Thus, make sure there aren't any scratches on the battery or the battery cable.

Solution 3:

You said you did a firmware restore, what I believe is like a hard reset and having all software and firmware brand new and even without jailbreaking it still shows same issue - restarting every 3 minutes.

So it must be a hardware issue and you'd have to send it to repair. Replace possible broken parts, figure out which one is the culprit and fix it. That's a lot of work but there's not much else that could be done, unless whoever opened the iPhone knew exactly what as done and then you could optimize which parts to try out. Yes, this can cost you good money both for the replaced parts and the labor work.

In the small chance that it turns out to be some part not related to damage caused by opening it, I would try to repack everything as new and returning the phone to warranty.

Fair is fair.

If you ask me and I'd have opened my iPhone and then broken it, I'd save my self the headache sell it to someone who do handle this stuff and buy me a new one.