Did you buy this new. If so it should of had a graphics card in it. If its burnt out you can replace it but its a major pain in the butt. You also would have to find the card that was offered with it originally or as an option.
Laptop graphics are pretty expensive also but you may be able to find one on ebay or get one from dell but that would cost even more.
There are several articles around about replacing them. Just look through some laptop forums and you can probably fine a guide.http://support.dell.com/support/edocs/systems/insN5010/en/sm/display.htm#wp1109848
I found out this is the gpu ATI Mobility Radeon HD 5470 .
If you just got it from dell and it quit working call them and get ot fixed.