Its been a while since I posted so a little update. I've replaced the capacitors in both power supplies and yet neither monitor will function. On one supply I replaced all the capacitors, and on the second I only replaced the three that showed visual signs of damage. With both the results were the same. No light output from the LCD, yet the "No signal detected" error was clearly visible with a flashlight. In addition, both power supplies now generate a fairly audible hum. I've got a few more tricks to try, but both LCDs (and the $50 I have invested so far) are not far from the dumpster.

