Replaced the battery, now iTunes doesn't see phone when hardwired

a dollar says you knocked off C300 or R61 with your finger or whatever you used to pluck the battery connector loose from the board for those following along with schematics.

For those without access to schematics, look where you stuck your booger picker or pry tool when you took the battery loose to the right side of the battery connection on the board. You'll have to look pretty closely because the component I think you flicked off the board is a 01005 package component . some magnification would be super handy. That one or two components you knocked off will have to be replaced.

This is a pretty common way to damage these phones which is why I know where to tell you to look. Now that you've found it, make a plan on getting it replaced. If you haven't done it before, you might want to look at having it done.