I have 2 monitors. I have 1 connected with a cable with blue plugs and 1 with white plugs that I think is called DVI? I cannot get either monitor to work with the cable with blue plugs. I can get both of them to work if I use the DVI cable.
I guess this means that my video card is busto as it is unlikely to be the cable at fault?
Don't see how you've come to the conclusion that the cable is OK by not getting a monitor to work with that cable. It's either the cable or the analog output on the card. To know which it is you need to test with either a new cable or a new card. It's more likely to be the card as there's not much to go wrong with a cable unless you have it all twisted up to break the wires inside, and video card/monitor cables tend to be quite thick and strong.
If it is a card then, yes, it is as simple as taking out the old card and slotting a new one in. You may need to uninstall the old drivers first but the new card will have instructions about that. I'm assuming you don't use this computer for games, as the Geforce 7300 LE is in no way cutting edge at all. If you're not going to use it for games then any old video card would do. Dual DVIs are available and there appear to be a couple for under £100 on dabs.com which look to be better than the card you've got.