When pressing the power switch you should have at least 2vdc on PS_ON to start the PSU.
If not then you could have a corrupt memory.
I have never seen a LC-37D5U becourse they was not sold in my country,
but I have seen other model with no led, no startup
and it was the NWM memory. Some of those
I could repair with I2C bus update method, one I had to change
to a preprogrammed memory.