I'd personally be reluctant to buy a computer from ebay. Regardless of that, the graphics card in that system is weak. The processor is ok, but you'd need a new graphics card if you want to play anything recent on even medium settings.
The PC is old (2007-2009 roughly) but was very high end then. You should be able to play any game its just what settings you can play them on. The CPU is still strong especially if you get it over 3GHz but the graphics card is quite dated now.
better look elsewhere and increase your budge. get an intel quad core if you want to play bf3 with anything near smooth fps. also look at a minimum of a gtx 270,gtx 450,gtx 550 or similar performing ati cards.
the fx 4100 is a dual core cpu in real terms. yes it has 4 cpus but there paired into modules. so they are comparable to a dualcore cpu with hyperthreading. which will be no good for bf3. you will get little more real world perfomance than the old 775 dualcores. so a pointless buy for bf3.
to play bf3 the minimum you need is a 775 quad core of 2.4 or faster
or a amd am2 quad core of 2.6 or faster.
4 gigs of ddr2 800 or faster.
a gtx 260 or ati 4890 or faster.
if you pick nvidia you want a minimum of a (x50 1s you get past the gtx 260) x60 x70 or x80 x90
for ati you need to get a x750 x760 x870 x690 perfereably the higher the fist number x the better for the lower numbers preferably 6 or better.