So you are getting it to reset. And when you see the Apple logo, you +let go of the two buttons+ and then press (and hold) the center (Select) and Play/Pause buttons, is the correct?
I believe your 20GB black U2 iPod is a 4th gen iPod. You can try opening it up using an online guide like this one.
http://www.ifixit.com/Guide/Device/iPod4th_Generation_orPhoto
So if you want to open it up... Be sure to use plastic tools as shown in the guide. You can get them from eBay for a few dollar. They usually come with replacement battery kits.
The two things you can try. (1) Disconnect the battery, wait a few minutes, and reconnect it. That does a complete powered off reset of the iPod. Without closing the case completely, try turning it one normally or putting it into disk mode.
(2) Disconnect the battery. Disconnect the hard drive from the ribbon cable. The other end of the ribbon cable is on the logic board, under a film. Peel back (but don't remove) the film to show the connection point. There is a tiny tab that you flip up to disconnect the ribbon cable from the logic board. Do so and inspect the connector; make sure there is no corrosion. Reinsert the connector and flip the tiny tab back down and re-cover with the film. Check the other end for corrosion and connect the hard drive. Reconnect the battery. Again, without closing the case, give it a try.
If it still does not work, it's hard to say if it's the hard drive or logic board that is bad, but it is more likely to be the hard drive.
I have successfully used a standard Compact Flash card in place of the hard drive, in a 4th gen iPod. You need an adapter like this one
[example on eBay|http://cgi.ebay.com/CF-to-1-8-HDD-IDE-Compact-Flash-Adapter
W0QQitemZ260386535142QQcmdZViewItemQQptZPCA_Cables_Adapters?hash=item26038653514 2&_trksid=p3286.c0.m14&trkparms=72%3A1240%7C66%3A2%7C65%3A12%7C39%3A1%7C240%3A1318%7C301%3A1%7C293%3A1% 7C294%3A50]
(I don't know anything about this particular seller.)
Mine only has a 4GB CF card, but bigger ones are getting cheaper, so I might eventually put a 16GB CF card in there. So if you like fiddling with gadgets, that might be a cool project. In the meantime, I guess would might need a new iPod for
normal use.