How do I check to see how long Windows 2000 has been up?

Use the command line utility called UPTIME. You can also use it to check remote machines.

UPTIME, Version 1.00
(C) Copyright 1999, Microsoft Corporation

Uptime [server] [/s ] [/a] [/d:mm/dd/yyyy /p:n] [/heartbeat] [/? /help]
server Name or IP address of remote server to process.
/s Display key system events and statistics.
/a Display application failure events (assumes /s).
/d: Only calculate for events after mm/dd/yyyy.
/p: Only calculate for events in the previous n days.
/heartbeat Turn on/off the system's heartbeat
/? Basic usage.
/help Additional usage information.