I guess it depends on the game. It's true that many new games are moving toward quad core cpu's though are those AAA titles what you have in mind for such a low budget gaming pc? My e8400 bottlenecked my hd 7850 a bit even when it was overclocked to 3.6ghz. It did ok on older games and was close to 60fps most of the time for things like halo, far cry etc.
A little confusion, are you talking about a q6600 or q8400? You mentioned a core2quad at 2.66ghz but mentioned the q6600 which is 2.4ghz, not 2.66. The q8400 is 2.66ghz.
Keep in mind that along with quad core cpu's newer AAA games are looking at more recent 3rd/4th gen i3's and i5's. There was a significant performance step from the c2d/c2q, the first gen i series and the first gen i series and the 2nd gen i series.
The q6600 vs a first gen i5 750
http://www.anandtech.com/bench/product/109?vs=53
And the q6600 vs a 2500k (stock)
http://www.anandtech.com/bench/product/53?vs=288
So yes, it's a quad core however it will get smoked by even old i5's that are the typical quad cores newer AAA games are referencing. The games you're likely to be playing will probably be older titles so no real demand for quad core and will benefit from higher clock speeds. The e8400 would be the preference. If looking at newer gen games I'd consider newer gen hardware. A pc gaming at all for $100 is a pretty big ask.
Just on a side note, I don't think the cpu is going to matter a whole lot. Doubtful the cpu will be the bottleneck, I was thinking the 7750 and 7850 were closer to one another than they are. I don't know what games you're intending for this, some 7750 benchmark scores. Quite a few games in the sub 30fps and closer to 20fps. It's getting into slideshow quality with fps that slow on some of these games.
http://www.anandtech.com/bench/product/535
I'm not sure what power supply came with that system since it didn't originally come with a dedicated gpu (even though the 7750 only pulls around 20-40w). There's no os included with that system so that will be another $80-100. Might have to find an old copy of windows that has the drivers for such an old chipset. It might be worth saving up a bit more money for something that will actually do what you're looking to do with it rather than invest $100+ into such outdated hardware that will have little to no resale value. Not trying to be a wet blanket here, it would be one thing if you had these components just laying around. That's not the case here though.