iPod touch constantly crashing

From what I've found on the web my problem isn't exactly unusual (if I got $10 for everyone who has the iPod crashing on him/her I'd be richer than Steve Bloody Jobs), however I haven't found yet any straighforward solutions.

My iPod touch crashes on a rather regular basis, but not when I have it plugged in to charge. Take the cable out with a fully charged battery, run FluxTunes (just to mention an app) and in no time I'm looking at a black screen. The only way to get it working again is to plug it in, press the sleep button, and then maybe within a few seconds I can enter the passcode and use the darn thing again, till the next crash.

1/ this ipod has not been jailbroken
2/ this ipod has the latest firmware
3/ it is the 3rd gen. model

So, anyone had the same problems and managed to fix it?
Do I need to move everything off and reset it?
Chuck it in the bin (after all, it was only $550...)
Try to get hold of Apple support (don't make me laugh!)

Any help greatly appreciated.

Cheers.