But since installing Service Pack 3 on this Win2k box, it now takes a long time to shut down. Before SP3, when I clicked "shut down", the OS closed and the PC turned itself off in just a few seconds. Now, it takes (what seems like) minutes before the PC turns off.

I'm having this very same problem with my win2k setup. Before the PC would shut down in say 10secs or less, now it takes about one minute or more.

I haven't found the answer as to why yet. But I do believe I didn't have this problem when I first installed SP3. I believe it popped up it's ugly head when I installed one of those pre-SP4 hotfixes that MS asks you to install now and then. (you know, with the little globe on the taskbar)

I've got eight of those pre-SP4 hotfixes installed, but I still don't know which one is the culprit. Havn't really had time lately to look into it either...
In my case it's certainly not a matter of old hardware since I've just installed a new mobo with an i845PE chipset.