First off some info on the machine would be helpful. Make/Model/Age/OS/etc... Recent problem, existing problem, past problems? It could be a few things. I'd first see exactly what the computer is doing. See if it still functions in Windows. If it's still working, you should be able to hear the startup sound, see some HD activity, and even do a "soft off" (press the power button and it shut down correctly). The keyboard should also work, so pressing things like Caps Lock should light up the lights.
You could also try pressing F8 during the boot process and enter VGA Mode. From there you should be able to reset the resolution and all to what you know your monitor can handle.