andypearce :
I know but my problem is that I have no 4 pin connectors on my PSU as far as I can see. Are there any other components that use a 4 pin connector so that I could just use a splitter?
I have a Compaq SG3 250uk
AMD Athlon II X2 220 Processor (2.8 GHz)
4GB DDR3 RAM
And I think I have an ATI Radeon 3000 Graphics Card.
I am trying to slowly upgrade the computer which is why I thought a better PSU with more wattage would be a good idea.
Hard drives, floppy drive (different smaller 4 pin connector though), etc... you can split from. I would not buy another PSU until you know for sure what other component you are going to buy. 350 watts may be adequate, or may be completely underpowered. Your next graphics card could need two 6 pin, 1 eight pin, who knows. You may need a 450watt power supply or a 600 watt one. I would recommend saving your money until you can purchase another component that will make sense to match your PS.
If this is your motherboard:
http://h10025.www1.hp.com/ewfrf/wc/document?docname=c02556928&lc=en&cc=us&dlc=en&product=4325599
well, don't bother spending any money. There is basically no decent upgrade path other than a new pc. Your expansion is limited to two pcie x1 slots, and the most powerful graphics card for that looks to be this: http://www.newegg.com/Product/Product.aspx?Item=N82E16814161354, a Radeon 5450.
You need to START with a new motherboard that supports your processor, which probably won't work in the case you have, and then get a new power supply, then new graphics card, etc... You are pretty much at buying a new pc by then. I've found ONE motherboard that MAY fit,
http://www.newegg.com/Product/Product.aspx?Item=N82E16813131659
Because your current mb uses SO-Dimms (laptop memory) it looks like.
Save up for a new pc.....sorry to give you the bad news.