Internal error when trying to renew a DHCP lease

Details

I replaced an old NE-2000 network card in my test computer with a new, 100Base-T card. Windows 2000 started without problems, and the new driver was installed automagically. However, it failed to pick up an IP address from my DHCP server. When I attempted to renew the DHCP lease from the command line (ipconfig /renew), I got the following error:

The following error occurred when renewing adapter <adapter-name>:
An internal error occurred.
Disconnect and reconnect the network interface or reboot the machine.

Rebooting did not solve the problem. However, when I made an attempt to manually set the IP address on this interface (to the same address that this machine used in the past), the cause revealed itself:

The IP address nnn.nnn.nnn.nnn you have entered for this network adapter is already assigned to another adapter <adapter>. <adapter> is hidden from the network and Dial-up Connections folder because it is not physically in the computer or is a legacy adapter that is not working. If the same address is assigned to both adapters and they become active, only one of them will use this address. This may result in incorrect system configuration. Do you want to enter a different IP address for this adapter in the list of IP addresses in the advanced dialog box?

So despite the fact that the old adapter was physically removed from the system, Windows 2000, with the memory of an elephant, insisted that its settings be respected. When I was configuring the new adapter manually, it at least gave me the option of setting the IP address to my choice anyway. However, when DHCP picked up an address on the same subnet that the phantom adapter was on, Windows 2000 (always picky about subnet conflicts) silently rejected that address, giving me instead that incomprehensible message about an internal error.