I'm running on an admin account in windows xp
When I try to use <WIN+R> key combo for accessing to windows Run Command box, I receive this message

"This operation has been canceled due to restrictions in effect on this computer. Please contact your system administrator."

If I open the Group Policy Editor and go check in User Configuration > Administration Templates > Start Menu and Task, all items there are "Not Configured" (same for the item called "Remove Run menu from Start Menu").

If I open the Group Policy Editor and go check in User Configuration > Administration Templates > Start Menu and Task, all items there are "Not Configured" (same for the item called "Remove Run menu from Start Menu").That setting is correct, "not configured" means it works normally. Enabling/Disabling the feature activates specific control, which you don't need to do.

I'm looking, but right now it I can't find anything specific to your problem in my resources, though I suspect a mild virus of some sort. If you can do a System Restore back a few months, that might be worth a try while I keep looking.

I would give this a try

Remove the virus-attack AFTER EFFECTS: Enable/Disable Run Command in Start Menu (http://xp-solutions.blogspot.com/2008/07/enabledisable-run-command-in-start-menu.html)

Or you can try running SDfix or smitfraudfix and also running a virus/malware scan to make sure your system is clean.

Agree with above, does the same thing happen when you click on start and then the run command?

This can be cause by a malware just like when task manager is not working, You can try running a anti malware software like malwarebytes...