KDS Monitor and 32" TV went out

[Nannuu]

I got one of the 21" KDS monitors a while back.  It worked for a few months but now it won't turn on.  I can hear it power up but no picture appears.  It happened once before but I got it to work after an hour of turning it on and off.  Now the picture won't come on at all.  I know it is not the settings.

My Sony 32" TV, it is about 9 years old.  It turned itself off a couple times but not won't power up at all.  I'd rather not trash it until I've at least tried a fix.

What is the first things to look at to figure out if I can fix them?

I know nothing about monitors other than decasing and installing computer monitors in Mame cabs.  Oh, and touching as little as possible, especially the suction cup capacitor.