Mac UI locked up. Are there any ways to unfreeze it short of cycling the power?

If you have SSH enabled on it, you might be able to ssh in from another computer and at least give it a graceful restart with, e.g., sudo shutdown -r now

Depends on what exactly has occurred. With Mac OS X would be unusual to see the entire system frozen. Much more likely a crashed app.

Have you tried a 'Force Quit' via command-option-escape?