In reply to Jamie Wakeham:
So the good news is that I have a 600W PSU (48A on the 12V rail), and plenty of room inside the case, so it looks like I could fit more or less what I wanted in there. A quick calculator tells me that with the 9800GT I'm drawing 27A, so there's masses of spare capacity for the new GPU. And I can see a spare 8 pin connector to the PSU so that's fine too.
But here's something I don't understand. I cannot, for the life of me, see where the current GPU is getting its power from. There is definitely no direct connection from the PSU to the GPU. Could it be drawing it through the motherboard? I thought that was only possible for very low powered cards - and whilst the 9800GT is not exactly quick, it's apparently using 125W; could it possibly be getting that through the PCI-E slot?