This sounds like a workgroup problem. If you are using Access security, you need to have all users join the same workgroup.
As a point of fact that might help you, I just learned that Access XP stores the default workgroup file (system.mdw) in the docs\settings folder of each users profile. (C:\Documents and Settings\UserNameHere\Application Data\Microsoft\Access) 2000 uses the same workgroup file for all users (C:\Program Files\Common Files\System\)
If you're not using access security:
Copy the file "system.mdw" from the XP machine onto the 2000 machine. (They may have different PID's)
If you are using access security:
Place the XP workgroup file on a shared network drive where all users can get at it, Do a search on the file "WrkGadm.exe" (this let's you change which workgroup you are a member of, it's path may be different depending on your OS / version of Office) Run this program, and join the workgroup you placed on the network. Do this for all users who need access to your database.
Be aware though, once you join a workgroup requiring a username / Password to login to your database, in Win 2000 and prior, anyone using ANY database on that computer will need a username and password to even open access. This is because 2K and prior only use one workgroup file for each computer, regardless which user is logged on. The way I have gotten around this is to use shortcuts to launch my databases with the "/wrkgrp PathToWorkgroupFile" at the end of the target line. This alleviates the need for joining workgroups.
Example target line for one of my applications:
"C:\Program Files\Microsoft Office\Office\MSACCESS.EXE" "I:\AOCP-POG_(4TH_POG)\~4th POG D-Base\New single app\Front-End\Battalion Application 2K.mde" /wrkgrp "I:\AOCP-POG_(4TH_POG)\Copy of SYSTEM_POG.MDW"
I know it's kind of long, but it's basically:
"PathToAccess" "PathTo.mdb/.mde" /wrkgrp "PathToWorkgroup"