My Inspiron 1721 has powered off without anything showing on the screen - please advise

My Inspiron 1721, which is now approx. 18 months old and of course out of warranty, powered off without anything showing on the screen. I am unable to bring the system up again. The power cord seems to be working properly. With battery installed and power supply plugged in, powering on the computer results in the power indicator light located on the right edge of the laptop is illuminated although no indicators above the keyboard are illuminated. It sounds like a fans turns on but nothing else happens, the screen remains black. Because of this I am unable to run the Dell diagnosis program.

I am not an expert obviously but am fairly desperate for any information the anyone might provide me.

What is the possible issue?

A place to begin would be huge,

Thank you