I had the same problem with my first touch, my screen then died completely. I took it into apple shop and they done an exchange. I'm typing on my touch so I can't copy and paste the full story. Grrrrrr!
Well, today i have witnessed the best customer service i have ever seen, in the shape of the apple store (glasgow)
I went in with my ipod as above ( no receipt may i add as it was a birthday present and bought from dubai ). guy that served me had a look and said the screen was totally dead, no problem sir, i'll just swap the screen out for you, it'll take 5 mins.
He then shouts me over and explains a slight problem in that there are 4 countries that are not covered by the UK warranty, so he was unable to repair the ipod. (UAE being one of the 4)
5 mins later i left the store with a brand new ipod touch, plus the software addons with the mail etc which i did not have on my original touch ( and gave me a new receipt )
It left me utterly gobsmacked.
Well done Apple 10/10. Amazing.