First, some questions:
1)When you first hit the power button, do you see your BIOS information, then your boot loader menu? Boot loader menu is where it says something like:
Choose or wait for default[Linux]
2)Do you see your init scripts load? Init script are all the messages and OK's or in some cases a graphical indication that services and hardware are starting.
3a)After you turn on your system and let the hard drive activity calm down, hit Control-Alt-F1 on your keyboard. Do you see a text based login screen?
3b)Does your text based login screen give you ANY indication of errors and/or warnings, or does it simply give you the Version of linux you are running and prompt for a username?
If you answered yes to question 1, then you know that your monitor and graphics card has at the very least some level of function.
If you answered yes to question 2, then you know for sure that your system is attempting to boot.
If question 3a is a yes, then your system is actually running, there is probably just a configuration problem with X. (X is the graphical system.)
If question 3b is anything other than "I see my Linux version and a login prompt", we need to know what the last few lines are.