well if there is no display on another known good monitor, then look for a problem the next level deeper. The graphic card, or most likely, the integrated graphics, would be what to look into next.
the more info you give, the easier it will be to diagnose.
Make, Model, S/N or approx age, OS, ?>?>?>??
Were there any problems before it failed to light up ?
Is the hard drive in use ? Listen carefully to the start up sounds. Does it sound like the hard drive goes through loading the operating system ? Any blinking lights ?
Reseat the RAM, and/or try to swap in known good ram. RAM can cause problems berore POST even starts. It might have been jarred loose, or it might be bad. Even try reseating the cpu.