How much room is there in your Dell - can you fit a dual-slot video card or are you stuck with single-slot cards only? What’s the wattage on the power supply?
Get some 650W 80% efficiency PSU for like $70 (Antec makes one, Earthwatts, that’s a good value). If you can’t fit a dual-slot video card, then you’re boned, but you most likely can.
Check for PSU reviews and then find something you want (650W is more than sufficient if you plan on keeping your case and upgrading components over time). My recommendation is the Earthwatts 650W:
Gotta be wary of the power requirements on the graphics cards - I called up the maker of mine before I installed it so I could be sure to know how much power they recommended.
This would work, in my opinion. You’d only need to get nervous about the power supply if you went with something high end (Ati 48xx/58xx, Nvidia 275, 280, 285, 295): those suck up to 200W, while the 5770 is rated for a 110W peak consumption (generally you’ll be well below 100W). And the good news is, you don’t need something faster than a 5770 with a 1680x1050 monitor.
I’d guesstimate your PSU can safely handle up to an HD 4850 or 5770 - i.e., anything with only one PCIe power connector on it. I’d go with a 5770, as it’s faster and uses less power, but you might be able to find a really good deal on the 4850 these days (no idea what video card prices are like in the U.K.). You could go higher-end, but then it becomes iffier if your PSU is powerful enough (and a replacement PSU eats into your budget) and I don’t know what’s available for under £200 that’s better. And I think you’ll find the 5770 plenty fast compared to your 9600 GT.