Restore doesn't work, and screen is completely blank.  Help?

Hi all,
I bought my iPod second-hand through Future Shop - a nation-wide electronics chain. It had been returned in less than 30 days after being purchased (the new iPod Videos had just come out). I foolishly did not purchase an extended product protection plan. What, I thought to myself, could possibly go wrong with this electronic gadget?
I shouldn't have tempted fate, I suppose.
Since purchasing it, I have had to restore it 4 times after a freeze. It has become increasingly difficult to restore it, or even have the computer recognise it for restoration, as time progresses.
At present, the screen is completely black, post-freeze. I have tried the "5 Rs", and various other iPod support documents. (I'd link them, but I can never find the same one twice. Maybe this is a good thing? I cannot use the Restore function because it does not recognise that I have an iPod connected to the computer, even though I have plugged it into various USB ports.
I have heard about letting the battery drain and then attempting a restore. Can anyone explain the reasoning behind this to me?
I do not know what to do. At this point, I just want to get rid of my iPod - and I haven't even finished uploading my music library to it - because of all the trouble it has caused me.
Does anyone have any new/different suggestions? Even links to help pages? Do you know if this is covered by the Apple warranty? I don't want to pay for Apple to tell me this isn't covered.
If you have been in the same situation, I would really appreciate hearing what steps you took.
Thank you!
  Windows XP  

Does your computer at present recognize the IPOD when it it connected?

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