....it has a better time displaying less busy images, like the ASUS screen or an input with no signal that just shows the input name in the corner. ...
1. I assume this monitor is NOT attached to the same system that was hit by lightening? Because the symptoms of displaying the BIOS screens sure sound like chipset/CPU/GPU video signal problem to me more than monitor.
Have you tried the monitor on more than one system? Of another monitor? Or another cable? Or if present another port? If you unplug the video cable from the powered up PC and monitor what does the monitor display?
2. Once warmed up the monitor works. I would surmise a cold short that when warms expands and makes contact restoring function.
3. I assume the warranty period is up? ...though if you let on the failure is due to lightening it is. Better start saving your shekels because you can bet whatever the problem is it will likely fail for good soon.