Your monitor is working OK but get no signal from the computer.
Does the fan(s) at least start to work?
If the fans don't even start to spin, your power supply is probably bad and need to be replaced. Get a new one of about the same power rating as your actual one.
Do you hear any beep sound when you try to boot?
If no beep at all, the computer is dead.
You need to replace the computer. Any drive is still good and can be mounted in the new computer if you get a desktop model.
Is it a single beep or several? Any dicernable pattern in the beeps? Some computers use LED codes. Normaly, they will flash briefly and go off or leave only the num lock one on. Any other pattern is an error indicator.
A single beep means a normal situation.
Your video card may have a problem, or you may have faulty RAM or some other problem.
In the first case you may have an unseated or dead card. Try removing the card and replacing it. If you still have no display, get a new card.
It may be a RAM problem or the memory moduls could be unseated.
In turn, remove each memory moduls and replace them in the same location.
If you still have problems, replace the memory (RAM). Take the ocasion to upgrade it to the largest amount you can.
If it's the motherboard, the CPU or some other component, it will be about impossible to correct and you'll need to replace the computer. The drive(s) should be OK.
Electro, October 2012