Going by what you have told us, I'm retracing the steps here.
You said the power comes on and the hard drive light flashes but nothing else happens.
You hear no 'beep' when the computer is turned on.
The monitor stays dark and the power light is on or at least in the standby mode. Normally the power light on the monitor is orange in color when it is in stand by mode and green when it is turned on.
Removing the RAM chips and trying them one at a time had no change.
Now for the possibilities.
1. The video chip on the motherboard is bad or has come loose from the motherboard causing it not to function. It is possible that if it has come loose from the motherboard that even putting another video card in the computer will not make the monitor come on for certain reasons.
2. The power supply has lost part of its voltage output. The power supply makes several different voltages depending on the part of the computer it has to supply power to.
3. Both RAM chips are bad. (doubtful)
4. The BIOS is messed up. This is the part of the motherboard that checks the functions of the components and verifies that they are ready to operate. Generally you will hear a single 'beep' denoting that all functions are normal. (also doubtful).
5. The motherboard had a voltage 'spike' and some components are damaged.
Generally, if you look at the little silver or black 'cans' that are soldered to the motherboard, the tops of them will be swelled up like a muffin. They are the bad ones and will need to be replaced. These are called 'capacitors'. They are like little storage batteries that help certain parts of the motherboard to operate.
6. As said before, even if the hard drive was bad, the computer would still show the 'post' screen. This is the first thing you see when you turn the computer on and it has your computer name on the screen. It also gives you certain options as in saying to press F1 for setup or ect..
Moving on to more things to try while you are waiting on the video card.
If you have a friend that has a computer who will let you try something,this is something to look at. Remove the hard drive from your computer and install it in their computer.If your hard drive is the same as theirs, you should have no problem figuring out how it hooks up. If it's a little different, you can ask for help or try to figure it out. Don't remove their hard drive, You will need it to load windows.
What you're looking for after you get the hard drive installed in the other computer is to look to see if anything is installed on your hard drive. This will be done the same as looking at a flash drive(usb stick) under the 'My Computer' icon either on the desktop or in the 'start' button at the bottom left of the screen. If you can read anything on the drive, then the drive is okay. Oh, try not to bang the hard drive around or drop it. They don't like that much,lol.
I'm gonna ask this because I ran into this before. Were you trying to restore the computer at the time it quit working? Reason is, if you were, the hard drive will read empty if you don't look for the hidden section of the hard drive where the recovery files are hidden. If you did not get any discs to restore the computer, they are on the hard drive on what is called a 'hidden partition'. I have actually ran into this a few times. People think something is wrong such as a virus because the computer is not acting right so they go for the full restore in hopes everything will go away. Sometimes this is true, sometimes not.
Going back to what I had said earlier about the video card in 1 above.
If the video chip has become unsoldered from the motherboard due to an overheat condition (which Nvidia chips can do) the computer may not be able to finish the POST test to start the system and default out. If the diagnosis is the video chip,it can be repaired at a shop.
You can try unplugging the hard drive and the cd/dvd drive from the motherboard.
Then try to restart the computer and see what happens.
On a rare occasion, if the battery on the motherboard goes bad, the computer will not POST. It is normally a CR2032 battery that you can purchase at any Radio Shack or such. If you had no problems with the computer retaining the proper time on the clock while the computer has been turned off for awhile, more than likely the battery is okay.
Sorry for the long post here. My mind went wandering!