That system takes a AGP slot video card, which is lots better than any PCI slot card, so stick with AGP.

Don't know what card you have now, but I can almost bet its one of the older versions and you may wish to upgrade if necessary.

You said the card, after trying a fix and succeeding for a moment until you moved it, might be telling that the card was not seated firmly ( A must ) or the card is going bad, or you need an updated driver, then again the cable could be going bad, and they do.  Jiggle the cables while the monitor is on to see if you notice some issues with the screen

Some times the driver for the card can become corrupted and all that is necessary is to download the same driver or a better more current one onto the desktop, uninstall the old one reboot the system and install the newer or even same driver again to see if this helps.

That system can take a nice 6600 nVidia card, or a better still 6600 GT one and keep the cost down.  Or if you want something better, a 7600 GS or 7600 GT card will be better depending what is done on that computer.  Let us know and we can suggest another card for you.

8300 Manual

http://support.dell.com/support/edocs/systems/dim8300/sm/index.htm

OK, try another video card driver.  Get a newer version from www.nvidia.com, have it ready on the desktop, than uninstall the old driver and install this new one. 

If that fails, time to look at another video card.  Unless you want to try and find another computer to test the card to verify the possible faulty card, or try another monitor hooked up to the card to see if its the monitor that is the issue.  Worth a try before getting a new card.