If you don't even see the boot sequence when you turn on the computer, its most likely your monitor. Double check the cables that connect your monitor to your computer, and the power cable from your monitor to the outlet. If everything looks OK, pull the cables out and blow in them, then plug them back in.
Resetting this connection is important, because the cable may be loose, so make sure you physically remove the cable completely, then completely push it back in.
If this still doesn't work, bring your monitor to a friend's (or 2nd) computer and try it again. If it still doesn't turn on, the monitor (or monitor cable) is bad. If it does turn on, you could have a bad power cable (the one that plugs into a wall outlet or surge protector). You can also try swapping out power cables with your friend's computer to help isolate the problem.