Assuming you can still read the BIOS (and also that you haven't tampered significantly with your video card bios) then you can find out what card you have through the system BIOS. Boot up your laptop and press F2 and somewhere in there it will list the system components and tell you what video card you have. Assuming you bought your 9300 from Dell, your machine can only have the integrated graphics, ATI X300, or the Nvidia 6800 go. If you have integrated graphics then you would have to replace the whole motherboard since your motherboard does not support discrete video cards. If you don't have an integrated graphics then read below.
The only cards you can use are:
ATI X300 (significant decrease in performance from what you have)
ATI X600 (very rare card and a decrease in performance from what you have)
Nvidia 6800 go
Nvidia 6800 go Ultra
Nvidia 7800 go GTX
for more details
These cards are listed in order of performance where ATI X300 is the lowest performance and Nvidia 7800 go GTX.
There was a lawsuit a while ago that required Dell to replace faulty video cards for free even if you are out of warranty, but I think that is only with the 7900 series cards (and their Quadro equivalents) on the M90, 9400/E1705, and M1710. If I'm right and your card isn't covered, then you want to go to ebay. Search for thing like "Dell 6800 go", "Dell 6800 go ultra", "Dell 7800 go GTX", etc. Just be sure to include Dell in your search because laptop video cards are not universal. Most companies use MXM for laptop video cards but Dell uses (or at least used) a proprietary connector. Anyway, because of low supply, these video cards are still pretty expensive.