Problem solved (I hope). Received a new power adaptor (the little square white box the power cord and the monitor plug into). Apparently, these units can go bad. Purchased the replacement unit through We Love Macs
www.welovemacs.com
$180 including shipping and tax
Monitor now works fine and does not seem to have the problem of turning on or not.
If anyone else is having any problems with the Apple HD Cinema 23" monitor not coming on, this might be the cause. I was having the same problem in my office when I was using it as my main monitor, which is OK 'cuz I bought a 30" monitor for the office... joy! joy!
Regards, Cyrus
iMac 27" Intel i7 Quad-Core; 16GB RAM; 2TB HD
Final Cut Studio, FCP X, Photoshop CS5, After Effects, etc.