Hi Doug Rudnik,
First of all thank you for contacting Fixya.com regarding on your TV problem.
You've mentioned that you can hear a sound for 1 sec and then the unit immediately turned off and there's a constant red LED lit. The symptoms you've described indicates that the main board of your unit is working fine and it automatically shuts off because it sensed malfunction on image boards. The constant red LED means that it is on standby mode only.
Now, since you've replaced the power supply board but still the symptoms persist, then the suspect is either the X or Y sustain board but high chance that the fault came from the Y sustain board based on my experienced. Y sustain board is located on the left side of your unit while the X sustain board is on the right side if you are facing the rear cover. These boards has a ceramic fuse(white color) and pico fuse(looks like resistor), please check the continuity of the fuses to determine which board gone to malfunction. If you found an open fuse to Y-sustain board then you need to replaced it. Blown fuse means that the circuitry on its line gone to excessive current.
I would advice you also to inspect the electrolytic capacitors on these boards. Most of the time loud pop came from a blown capacitor and has a physical indication of fault like bulged/dome at the top and can be easily identify through visual inspection. It can give you an idea also which board gone to malfunction. See sample picture below of faulty electrolytic capacitor with bulged dome at the top.
Here's the link for X and Y sustain board.Y sustain boardX sustain board
Hope I've gave you an idea what's going wrong to your set.
Have a nice day and take care!