You don't, some graphics cards need a seperate connector as they can't draw all the power they need through the motherboard. The 7600GT does not need it as far as i can see from reviews.
http://www.guru3d.com/article/Videocards/326/
You
could carry the RAM over, the old AMD socket (939) is compatible with DDR 3200 which would save you around £60. It's also pretty competitive with the newer AM2 socket, not much difference in performance. But you lose the upgrade potential of AM2.
939 3800 X2 £117
Asus A8N-E £64
1GB Cheap as chips RAM £65 (to add to your current 1GB RAM)
Leadtek GeForce 7600 GT £124.49
Seasonic S12 380W £50 (ish)
Total = £420 + shipping
Or tw1ggy's build:
£111.57 AMD Athlon 64 X2 Dual Core 3800+ 2.00GHz (Socket AM2)
£58.69 MSI K9N Neo-F nForce 550 (Socket AM2) PCI-Express DDR2
£124.49 G.Skill 2GB DDR2 NR PC2-6400 (2x1GB) CAS5 Dual Channel Kit
£124.49 Leadtek GeForce 7600 GT 256MB GDDR3 TV-Out/Dual DVI (PCI-E)
+
Seasonic S12 380W £50 (ish)
Total : £470 + shipping
You could probably get away with your current PSU. The 7600GT is a very power efficent card, and AMD CPUs aren't very power hungry. Do you know what model you have? tw1ggy's option would be better by a few % and give you much more upgrade potential for the future. Or there are cheaper PSUs that will do the job for less money, notably less (£25 or so i just like seasonics

)
Another thing to note is that the odds are a dual core CPU is a waste of money. What are you planning to do with the computer? Internet surfing, gaming and normal office type applications do not benifit (noticably) from dual core. If you got tw1ggy's build with a cheaper CPU then you can always upgrade it later...