I got my friend monitor LG 31MU97 with the same problem no power and LED light.
I just use PIN point test use service manual for LG 31MU97.
And i found what CPU stuck in boot loop with error report. So i just updated Firmware in ROM in IC205 (MX25L8006E) it have error checksum before. It is 1 Megabyte rom.
And after update everything works again.
I did it with two my friend monitors. It is common problem how i see.