Mysterious permissions issue on Win2k3 server

The setting: small high school computer lab; new server with Win Server 2003 installed; it is a member of the domain; I log into it using domain admin credentials. So far no problem. I download an exe or bat file onto the desktop (or anywhere on the drive). I check properties of the file. Security – admin has full control. But when I try to run the executable I get a message “Windows cannot access the specified device..you may not have the appropriate permissions.” I have tried several different files, both on the desktop and in folders at the root of the C drive. Same message. BUT…if I copy the file to a flash drive and run from there, it will work without complaint.
Any ideas what’s going on? It’s driving me crazy!