Alot of motherboards still show a sign too distuingish whether video card or RAM is dead, if you can't see anything on the monitor i'd look at the video card first.
First things first, unplug the monitor cable in from power AND cord in the back, it may sound silly but I thought my video card was dead and all I did was replugin in the power and it worked fine.
If no luck (probably wouldn't), try this;
Make sure when you open everything up to unplug the power from the back, and then touch the power supply (supposedly grounds you), now unplug whats at the back of the video card, open up your case and if you feel confident doing this;
firstly get a screw and unscrew the screw holding the video card onto the metal case framework, then gently pull the video card out, you can do this by just grabbing metal bit on the side, and the other side grab the flat circuit board, now in a FLAT manner, pull, you can gently pull by just pulling out small amounts from left hand side then right hand side alot of times
examine the card, if you see any burn marks, try to spin the fan with your finger(if there isnt any dont worry), if there's a heat sink blow on it if there's any dust, make sure everything looks alright (just see if capacitors are in tact etc..)
place the card right back in the same way and put the screw in, and put the case back, the monitor back and try again
faulty ram for example on my system still boots up onto at least bios and tells me, OR what im assuming everyone saying it being either RAM or video card, could be the beep code, what motherboard do you have on that computer?
you can always call a computer tech but they charge alot, i can trouble shoot it for free if you want, but you bring it too me