Screen failure

I am about to replace my ageing pc & monitor, but need some interim assistance please.....
My screen keeps dying, and I am unsure whether it is the 15 year old monitor or the onboard graphics of a ~5 year old mobo.
After PC is on with monitor off, when I arrive home from work and turn it on, after a short period the screen slowly turns black, indicating to me that the it is due to overheating of the mobo, any ideas?
Any diagnostic checks that I can do to determine which I need to fix?

 

Do you have another monitor to try or barrow?

15 years old for a monitor is a long time!

 

No, not yet, will try & borrow from work.