RCA DLP Model # M50WH74S Problem: Replaced blown lamp, when plugging it into AC, blue LED lights up right away for 2 or 3 seconds, then shuts off. Waited for a few seconds, and relay will click on and off ( blue LED indicator is not lit even when pressing the power button). But,TV is still dead.

The blue led dies because the power source dies: it detects a big short on one of its outputs and shuts down to protect itself automatically. Since apparently it's a very big short and you just had to replace the bulb then the faulty part is the ballast board (the one that powers the bulb): when the bulb failed it has generated a power surge that fried it.
Replace the ballast and verify the power source board: if you're really unlucky when the ballast got fried it has in turn damaged the power board.