I am sorry to hear about your iPod touch not wanting to come on or sync for you but I had a few questions to try to isolate what is causing the problem.
'''Questions:'''
What version of iTunes are you running on your computer and firmware on the iPod?
Do you have a Mac or Windows PC? Or is it a laptop?
Have their been any recent repairs on the iPod?
These questions will help see if there is a compatibility issue with the equipment and/or software. If there have been recent repairs, it might have been damaged more or they only fixed part of the problem. I also have going to post a guide by a member who talks about their iPod shutting down or not wanting to come on.
[guide|51353|Click here to be taken to their guide.]
Other than troubleshooting, I would recommend contacting Apple or your phone company to see if they have additional resources you could use.