My Sony SDM-HS74P display does not stay on.

I have the same issue and wrote the monitor off for now after checking all cables (and a different computer). The logic circuitry and panel are sill ok as I can see a faint image with proper lighting and close inspection, but no backlight makes it useless.

Since there are 4 lamps (CCFLs) on this model, the problem likely is not there but on the inverter circuitry driving them. This does not look easy to replace as this is part of a bigger board.

It looks like some could repair by changing a few (or even one) component on the board, but unless your are used to this (de-soldering and soldering back), you are kind of stuck.

I will attempt this if I have time as I hate junking 99.9% ok hardware. In your case since this is an old monitor you should just replace it if not technically (on the electronics side) apt.