iTunes isn't recognizing that my iPod is plugged in.

I've got an old iPod Touch 3rd generation. My friend gave it to me a while back and the power button has been messed up and such so I can't use it but the iPod itself still worked. However, a while ago it stopped turning on. I plugged it in because I thought that it was dead. It light up, showing the charging screen but then after charging a bit, it'd show the connect to iTunes screen instead of turning on. I've tried on multiple occasions to plug it into iTunes and it doesn't even show up on my computer. It still lights up as if being charged when I plug it into the computer, but my computer won't pick it up at all. I can't reset the iPod either because the home button doesn't work. Any help would be appreciated. I am using a Mac.