iPod Touch 2G 32GB stuck on Apple screen, unable to restore

My iPod Touch froze a few days ago. Powering off/on did nothing (I can't turn off using just the power button, have to use Home as well). Hard reset does nothing - it just sits on the Apple screen, without even a progress bar. I let the battery run out, and have charged it again, with the same results.

I was trying to avoid connecting it to iTunes (a whole other story, basically the laptop with my existing iTunes library bluescreened, I thought I had it all backed up but turns out the apps and backups aren't there, we're working on data recovery) but figured that was my only option to restore. Not sure whether the fact I've never connected this iPod to this PC is a problem, but it is not recognising it at all. Not just in iTunes - it's not even registering as a USB device. I have tried forcing it into Restore mode to get it recognised, but it just goes back to the Apple screen and sits there again.

Any ideas? (It's long out of warranty).