What resolution are you currently running?
Off hand all you should need is a new graphics card.
Probably a new PSU for safety
And a new case.
I say a new case because while the Dell Studio 435mt is a standard, if a bit small, mATX case and the motherboard is a standard mATX size the pci-e slot is lower down than normal, this means that if you get a new card it'll be twice as thick which would put the air intake for the cooler flush against the bottom of the case which is going to cause air flow issues.
On top of that is the hard drive mounting method + narrowness of the case means most cards are not going to fit unless you remove the bottom hard drive.
4gb of ram is still plenty and should have any major impact on games, however I would investigate what form it's in because the x58 can use triple channel ram, ie 3 stick per set not 2, you really should have 6gb (3x2) or 12gb (3x4)
New case + psu £90
http://www.ebuyer.com/250952-coolerm...rc-502-kwa1-jp (psu is a bit OTT but it's a good price and better cooling than the stock dell case)
£140 ish for a gtx560
http://www.scan.co.uk/products/1gb-k...-mhdmi-plusfre or 6870http://www.scan.co.uk/products/1gb-xfx-hd-6870-4200mhz-gddr5-gpu-900mhz-1120-cores-eyefinity-hdmi-2x-mini-displayport-2x-dvi-i
Ram depends on what you currently have but to buy 6gb (3x2gb) of 1600mhz is only £35
http://www.scan.co.uk/products/6gb-%...-9-24-xmp-150v although check first you may well just be able to buy a single 2gb stick to add in to get you 6gb, just remember to match speed, cas and voltage and you shouldn't have a problem. (fully matched sets are really only needed when overclocking)