Why won't my iPod touch turn on after I replaced the battery?

It's hard to tell what could be wrong because no one else knows what your soldering looks like. Things that can go wrong when you do this repair are that you could have torn one of the pads off while unsoldering the old battery. you could have overflowing solder that could be touching the other pads. you might not have a complete connection with your solder. I would check the voltage of your new battery and make sure its sitting somewhere around 3.7. That would tell you whether that battery is good or not. Other than that it's hard to give an answer without seeing the solder job.