Is it an actual, real server hardware wise? If so, check any remote management devices, like a remote insight board (HP) or DRAC (Dell). Some of the older ones had some odd cables that had to be hooked up just right. Also check for VNC or any other remote control programs (outside of Terminal Services).
Also, is it attached to a KVM of some kind?
It's hardware, a Dell. What's this "remote insight board?" No, there is no KVM, the keyboard and mouse are plugged directly in. I'll check for remote software tomorrow morning, but I would assume that wouldn't start before the computer is logged into. The behavior starts the instant the mouse cursor appears, before "Windows is loading your settings" or whatever.
I think the obvious thing, after resetting any attached KVM switch, is to remove the PS/2 mouse entirely, disable it in the BIOS, and attach a USB mouse instead.
Yes, and that's what I did. I only mentioned disabling the PS/2 ports, but I also attached a USB mouse.