Ubrales is right, we might try some extra things to doublecheck though.
I believe it's a Dimension for the model#.
Try this monitor on another system if you can. I've seen screens being on just for a moment & then going off. If picture stays up, sure it's an issue w/the PC itself, otherwise, u can think about replacing the monitor itself & keep ur computer for longer.
Otherwise,
Check if the power light on tower stays on or not, & whether it blinks or not.
A Green light means power's going thru the inside fine (most of the times), Amber means we have a component going bad or a short we can resolve by reseating internal stuff.
After that, check the back panel LEDs. These PC's should have some LED indicators on the back I believe: A, B, C & D.
Write the combination (last one after u turn the system on) down & post it.