It sounds suspiciously like the graphics card in my brothers computer (a HP Pavilion Elite M9175.uk-a) has died - no signal over any of the outputs while the rest of the PC appears to be running fine.
The machine has a Core 2 Quad Q6600 processor/G33 chipset which means it's only got 1 16x PCI-e 1.1 slot and a 300W power supply. 3GB of RAM and the existing card is a GeForce 8600GT.

So, any suggestions for a cheap and cheerful replacement graphics card that'll work with the limited resources available?

I've no idea if it would work, but someone gave me a graphics card a couple of years ago that I have no use for which is whatever came after agp. Pm me your address and I'll send it to you.

I've got an old 6200 if you just need something that works

Thanks for the offers folks.

Apparently there are onboard graphics on the MB but they won't work if there's a card in the 16x PCIe slot so I'm going to remove the 8600 and see if we get anything over the onboard graphics (i.e. if it is just the graphics card or if the machine has a bigger problem). Should have an answer by the end of today provided the snow doesn't get too bad.

In other news, he's got Windows 8 Pro (32 bit) on there if that's likely to cause any problems.

A wee update.

Was definitely a borked graphics card. Pulled the card and connected to the onboard graphics and hey presto all working again.
As a tier 1 manufacturer I was expecting somewhat better internal build quality from HP (I guess Apple have spoiled me in that regard). Cables everywhere including a large loom from the PSU over the top of the sodding graphics card which made it real fun to remove.
Onboard graphics are Intel X3500 or something along those lines so I expect that gaming will be something of a problem.

So, I was having a bit of a look around 'tinternet and wondered if an AMD Radeon HD7750 would be a good choice (mainly because it doesn't need any ancillary power connectors which I couldn't find in the case (max TDP of 55W) and it would represent a decent improvement over the old card and the onboard graphics)? Would it be alright in a PCIe 1.1 slot (given that it's a PCIe 3 board)?

PCI-e 3 is backwards compatible with older versions