Monitor dies after 5 min?

On the basis of such a wealth of troubleshooting and diagnostic info, it's hard to say ;-)

It sounds like a thermal fault. I'd guess a capacitor is breaking down when it heats up. Or possibly a marginal solder joint, IC or whatever. It could be just about anywhere if it's a shorting component causing shutdown- switchmode power supplies are designed to shut down under excessive load conditions.

The good news is that thermal faults are often very easy to fix- a can of freeze spray and a heat gun should pinpoint the fault in about 5 minutes. The repair should be straightforward and not very expensive.

OTOH, the flyback/LOPT insulation could be breaking down, which will cost a relative fortune to fix. Are there any symptoms at all prior to it shutting down?

Dave