Problem: SQL Server Service will not start due to expiration of evaluation period.

Desire: To obtain some “grace” for the evaluation period and then add a License Key.

Remedy: You’re going to need to acquire a License Key for the same version or later and then perform an Edition Upgrade (if you’re staying with same Version) or run Version Upgrade (if you’re going to upgrade from 2005 to 2008 or 2008 to 2008 R2, etc) from your installation media.
Barrier is – upgrade will fail on SQL Service Health Check because the SQL Service will not start since it’s been deactivated – OK, NOW WHAT?!  My solution to obtaining some “grace” on the activation period was to disable the network adapter, roll the system time back to a date that was within the Evaluation period and RESTART the server.  After the restart, Check to see that your SQL Service started and then run the upgrade from your installation media.
After setup completes, set the time back to current, enable your network adapter and restart the computer.