|The computer will work fine without a cover. You just need to be careful that nothing spills/falls into it. Some Dells have an intrusion alarm which is just a switch that tells the bios the case is open or was opened. If yours is that way you should be able to disable it in cmos/bios setup or just remove the switch.|
Otherwise you'd need a different case (might be hard for a Dell) or different video card or maybe a modified cover.
You're not really green until you're soylent green.