I have not experienced the total blank screen, but I have had them lock up on me before. There is reset procedure, but not sure if it would help you if you aren't able to power it on. Not sure what model you have, but here's the procedure for the classic:
http://www.apple.com/support/ipod/five_rs/classic/# Wasn't sure from your description, but have you tried connecting it to your computer? If you turn it on while connected, you might be able to open it up under iTunes and troubleshoot from there.
You might also try toggling the hold switch - sometimes, even though it may be in the unlocked position, it gets confused!
And then there is the possibility the battery may just be totally dead, and unforutnately most models you can't replace them yourself.
Good luck!