I built my nephew a budget gaming rig. Athlon x4 II 640 3.2Ghz(quad-core) and an HD5770 1GB.
I am well aware that the 5770 is not powerful, but bare in mind that he plays on a 17 inch CRT monitor @ 1024x768 so it's not 1080p or even 720p.

I have not measured the FPS, but trust me, it was low enough to notice it. I say <30. Is the card not powerful enough or the CPU or both?

I played C2 for over a year with a 5770, minimum settings @1600*900 50-60 FPS, and I was recording too... So it can do it.

The question is, why doesn't it? The Athlon CPU does not have L3 cache I believe, but I certainly don't think that's the problem(though it starts waay slower than on my system). It has 4 gigs of ram, running Win7 x64 and yet...

In case you don't know lower the res, the more cpu bound games becomes.In your case the slow cpu is bottlenecking that card badly.And yeah MP is always more cpu bound than SP.Strange it may sound you can get better performance by increasing res.

I don't know how old the screen is, but old screens with low res often have only 30mhz

I am aware of that. As the resolution goes lower, the GPU actually performs faster, so the CPU receives the data faster but it cannot perform as fast(sending new data back to the GPU fast enough to draw).

I have a dual core processor (Core 2 Duo E8400@3.3 GHz) and the same GPU (a bit overclocked, 950/1350 IIRC). I usually play at High settings (lowest in the options menu, not low graphics script), 1280x720, and performance is OK (40-50 FPS, I haven't measured it recently), but sometimes I get frame drops in the 20's, I guess these are CPU-bound. I'd expect a better performance from a quad-core CPU as your friend's, even from a low-performance one, as Crysis 2 performs much better in quad-cores than in dual cores.

Are other processes stealing CPU power? Are CPU/GPU temps OK?

Installed chipset drivers and gpu drivers?

Obviously. Without the GPU drivers, game won't even run and the visual effects in any Windows will lag like hell.

and what about the amd chipset driver (motherboard)?