I have an iPod 2nd generation 20GB (2004), it's hardly been used and hasn't been updated to my iTunes library or charged up for about 4/5 months, I've just tried to charge it up and update it but there is absolutely no response, no Apple logo, nothing, it wont charge and nothing comes on, it's just a completely blank screen. Suggestions say to jiggle the off/on switch and hold down the select/menu for a number of seconds, which I've done, nothing. Also to try and charge the battery up or attach to the iTunes library to try and restore, nothing it didn't even register or recognise the iPod in the library. I tried the 5 R's but NOTHING! Please can someone advise, is it a battery problem?
That really sounds like a battery issue. I could be a dead screen but since you mentioned that it doesn't show up in iTunes I believe it is just dead right now. Take it to an Apple Store nearby and ask somebody at the Genius Bar for that. I am sure they can help you if it is just a dead battery.