Concur with all that Agent86 says. I regularly run just such an arrangement when I'm "on location" but the two cards I use (3Com and D-Link) have a kind of "dongle" that enables me to connect either co-ax or UTP.
There is a "gotcha" that you've probably sorted if you've succeeded in getting them to communicate with UTP but I'll mention to help others.
The default Network Guest Account setting in Windows 2000 is "Disabled". If your machines don't recognise each other, it may not be because of the connection but the system settings. This is easy to fix in Control Panel/Administrative Tools/Computer Management/Local Users and Groups/Users and double-click Guests in the right-hand pane.