I replaced the battery in my iPhone 4 the other day. It seemed to work fine till it ran all the down yesterday. Upon plugging the phone back in it got itself stuck in an infinite loop of rebooting.
I placed the phone into restore mode and plugged it into the computer, but it wouldn't get past the extracting and preparing software phase with a "2001" error. Which Apple says is something to do with USB. Much trying with new cables and restarting resulted in nothing.
After switching back to the old battery though I was able to restore the phone (and I wonder if I had though to do that initially if I could have kept the things that hadn't been backed up that day, alas) but I still wasn't able to reload it from the last backup because it refused to show up in iTunes.
Finally i noticed that it was showing up as an empty iPhone in Aperture which was running in the background. After quitting that and restarting iTunes I was able to make it show up and am running the restore now.
A tower of unrelated problems is so much fun to tease out.
So... Bad batteries can cause the phone to refuse to connect properly even when connected to power. And Aperture (and probably iPhoto) running at the same time can keep an iPhone from showing up in iTunes if it's been just recently restored.
Putting that information out there for any others that might find themselves in a similar situation.
I've heard back from ifixit.com from where I got the original battery, and I'll give them a plug for the best support ever, just shipping me a replacement and no hassle. I've used these guys many times in the past for parts and tools and never had an issue and the one time I did they really came through. I know you can find the batteries a little cheaper if you're willing to order direct from china or go on ebay, but their wonderful takeapart videos and their wonderful support are more than worth the extra few bucks. Support a company that will support you back!