That's good. So it is not a hardware problem, and it is not an overall system problem, just something in your current user account. It may be a program or background process, but it may also be a specific user preference file that has become corrupted or mis-set.
If you are hunting for the process, you should open System Preferences
Accounts pane +Login Items+ tab and check the list of items. Make sure everything that starts automatically upon login makes sense.
On the preference file side, it would make sense that the preference is related to using the Apple Remote. Try these procedures related to pairing the remote to the computer.
http://support.apple.com/kb/HT1619
Your remote seems to be working with your computer, but maybe if you unpaired it and paired it again, the current preference will be over-written and the remote will work 100%.