Okay. First things first- you can't run the card positioned like that- it will warp the PCB (circuit board) assuming you don't break something first.
On this page
http://www.gpureview.com/geforce-7600-gt-pci-e-card-385.html
Look at the image that has the card (there are 2 in this instance set up for SLI) set up on the motherboard,
I presume the problem is that the tongue of the plate (where the monitor connectors are)- the metal tab that extends below the motherboard- won't fit into any corresponding slot between your motherboard and the case. If this is correct you will need to modify either the case or the card backplate,
The easiest solution for a novice would be to remove the card from the computer and put the card into the anti-static bag it arrived in.
If you feel confident enough in your ability then either remove the faceplate or keep the card wrapped in the anti-static bag with just the faceplate showing, use a low-tack masking tape to seal the main part of the card in the bag and mask the DVI and S-Video connectors (where you plug the monitor cables in) and very carefully use -in order of preference:
Dremel/Rotary tool with cutting disc to cut the tab down/off
A fine tooth blade in a coping saw or similar.
The hard part of the operation is holding the card carefully but securely while doing this.
It may be worthwhile going to a light engineering workshop or similar and getting them to do it if you don't have the right tools to hand.
The other alternative is machining a slot in the chassis to accept the tongue of the faceplate. You would need to take all components out of the case and unless Dell have changed their case design radically the steel they use is brutal and difficult to modify/cut.