My main desk video monitor, a PVM-5041Q has recently started having a few issues. The issues it's having are that it refuses to power up, both in 12V and the internal mains power supply if started cold, and/or after a few days. Staying on for five or so seconds and turning off, and the second issue is that the PVM keeps losing Vertical Hold when running over RGBS when the set heats up after running for 20 min.

Anyone know what might be wrong with my set? It was working good for a while and then started doing this.

You're probably going to have to change some capacitors on both problems.
These are little hotboxes. This is what happens when you try to put 10 lbs
of $#!+ in a 5 lb box.
I found the manual:

https://archive.org/details/SonyPVM5041QPVM6041QOperationInstructionsAnd6041Se rviceManual/page/n37/mode/2up

Good luck.