I finally found the time to replace the internal power supply with the replacement I bought online. The display has been functioning fine with the new internal power supply for the last 2 hours. I believe it is now fixed. I used the "new" version of the power supply, part number 661-5543, and purchased it from the DV Warehouse website.
Obviously there are no directions with the part, but you can follow the dissassembly process on the iFixit website and simply replace the power supply board with the new one rather than putting the old one back. The process was fairly easy if you have just a little mechanical/electrical skill. You need a suction cup to pull the screen silica off and a star bit screw driver. I don't remember the exact size star bit but it was a common size.
Everything is working fine now. I can post again in a couple days to confirm that it was the issue, but I am confidant that it was. Hope this helps some others.
Note on troubleshooting before replacing power supply -
I saw some posts online that this issue can be cause by a fauty cable set that plugs into your Mac and for some, if you move the cableset just right, the screen would work again. That was NOT the issue for me. I ruled that out in my troubleshooting by keeping everything perfectly stationary until the screen went blank. Once it did, I used the power switch on the power strip the cinema display was powered by to cycle the power to the display without touching the cables on the cinema display. My display would come back on for a little while which led me to believe there was a power supply issue.
Note on power supply -
There is a NEW part number from apple that I used above (661-5543) which replaces the original part... Though this is common, it does make wonder whether the original design is faulty or otherwise less superior than it should be...