iPod touch stuck on restore screen
It sounds like the home button still works, which is the only button you need to have iTunes recover the iPod for you. Note that recovering the iPod will wipe all of its data completely.

I tried this with an iPhone which I believe was in much worse shape than this and it worked. In my case my phone never got past the Apple logo and would shut down shortly after. Even a hard-drive restoration company wasn't able to access the data, yet the recovery through iTunes did work, so there is hope.

Apple calls this recovery mode.

All you need to do is press and hold the home button on the iPod while connecting it to the PC. iTunes should detect an iPod in recovery mode and allow you to recover the device (again, this wipes out all data completely).