My imac 24 inch intel core 2 duo 2.16, with 10.7.5 wont shut down

https://discussions.apple.com/docs/DOC-6921 reveals many reasons a machine might be slowing down, which can also affect if it shuts down or not.

Press and hold the power button for a few seconds until the power shuts off, then release, wait a few more seconds, and press it again briefly to restart.