... The computer boots up without a problem but now my monitor just gives me a black screen....
How do you know the computer is booting up without a problem? Did the computer boot once or more with the new RAM installed?
In any case, first thing to do is to check connections (make sure the graphics cards VGA/DVI connection is not connected to the on-board graphics card if a full graphics card is available).
Next, try a different monitor.
After that re-seat all expansion cards and RAM.
Failing that try a minimum boot, unplug all hard drives, CD drives, all but 1 stick of RAM use the on-board graphics if available and not already in use. If that works then slowly add things one by one to find the problem component.
If that fails then reset the CMOS by either pulling the battery out for 2 minuits or using the reset jumpers (shown in your manual).
Finally try a different power supply.
If you are still not getting anywhere then it's time for a new motherboard.