My parents computer can do this and this is how I have done it. They have a Dell Dimension 2350, specs in my signature.
Go to Start >> Control Panel >> Double Click System >> Choose the Hardware tab >> Device Manager >> Expand Display Adapters >> Right Click on the onboard video adapter >> Select Enable.
Your Computer may bring up an install Wizard, just follow the wizard and install the card.
Turn off your computer
Then, Hook which monitor you want to which video card. And, Start the computer.
If you want the exact same image on both screens you are done.
If you want to be able to drag windows to and from each monitor, and/or have seperate windows open on different monitors Go to...
Start >> Control Panel >> Double Click Display >> Select the Settings Tab >> Click on the box to the left there should be two of them. Now make sure you have "use this device as my primary monitor" checked and also have "Extend Windows Desktop to this monitor" checked.
Now, click on the box to the right (the second monitor) and make sure you have "Extend Windows Desktop to this monitor" checked.
Click Apply, your screens may flicker and or go off for a second but don't worry, that is normal. If asked, say you want to keep these settings if you are prompted.
Click Ok, close everything out. Test to make sure you can drag a not fully maximized window/program to and from each monitor.
If your start button and task bar is on the wrong monitor, then go back into the Display Settings and choose the opposite box you have selected for the "Primary Monitor".
Let me know how it goes, or if you were even able to get the on-board adapter enabled.
Edit: If this doesn't work, you could probably pick up a graphics card that has dual heads, just hook both monitors to it and follow the same instructions as above. I believe my local computer store sells 6200 series for $25. Newegg.com
I'm sure has some good deals on cards that are the same series as what you already have and/or better.