I just bought a used 2001 and have tryed with several games to go into multiplayer and log in ..it all works up to "logging in" internet connection is established but wont connect
You might want to post this in the psp networking area. Since you didnt give much details im going to guess that your having problems connecting your psp with your wireless router or that you might have forgotten to turn on the wifi switch in your psp.
Now if you do have a connection to the servers it might be the older games are no longer avalible for online play. Or that your games need full PSN login so your psp needs to be registered with the psn. Its a mix of things please give more details.