iPod Touch 4Gen Won't Turn On

My iPod Touch 4th Generation won't turn on. I've tried almost everything I could find with a Google Search. Also, I have dropped it once or twice in the past, but It has worked for a while afterwards. The screen digitizer is still cracked from most recent drop, and I am waiting for the replacement to fix it myself. I feel very stupid having to post this problem, since there are other posts, but none of those (that I found) are about this exact situation, and none of those fixes worked (things like holding the Power and Home buttons, etc.). Although, I have not tried doing anything with iTunes, for a few reasons. One is that I could never get an answer to the question of whether this has to be the computer that it is synced to. That computer has had a new install of windows, and is not working well right now. Also, while we are at it, can you sync your iPod to a different computer than it was without reseting it? I have authorized other computers, but I don't think that that is the same as syncing, is it? I suppose that I could try using a different computer. Ubuntu is on my main one, but I have access to computers with Windows 8 and XP, as well as my old PowerPC G4 Quicksilver 1GHZ Dual Core with OSX 10.5, and my other PowerPC Macs. Also, what should I do about using it on Linux? Can I install iTunes in Ubuntu? I've heard of people doing it using Wine, but haven't tried it yet. Or, should I use a different program? Sorry for all of the questions, I guess that I have just built up all of these questions over time, and never found good answers on Google. Thank You all in advance!