My 4G iPod (black and white screen, but with click wheel) has had this issue for the past 2 years and 3 months.
Yeah, very annoying. Basically, I can't turn it on if I haven't used it for awhile. Say I charge it for 3 days without using it. If I try to use it, it won't turn on regardless of all the little tricks people use to turn it on. I know people here would tell me to do the things I was already aware of, so I never even bothered posting the problem here and decided to just deal with it.
However, once I plug it into a wall socket or my computer, even if it's only for less than 1 second, it's fine. And if I turn it on the next day, it's still fine. It's only an issue if I leave it unused for 3-4 days or more.
Once that Red Nano comes out in Australia, I might get it. That, or just a 2 GB grey iPod Nano (ie: the poor boy "ghetto" one)