Dreams, dreams, dreams well maybe not but you'll have to look around alot for ocassions as prices changes alot and not always going cheaper.:]
Can't give you links to shops, not gonna waste time looking
it's your build soo waste your own time for it
, but some tips to get into that $300 below.
Maybe some AII X2 around 3ghz in stock in some cheap asrock am2+ mobo, but then again not really worth finding mobo with ddr2 as it'll slow down your system. Soo most likely you would also need 2x2ghz ddr3 ram(just buy 2 lesser not 1 higher to set them in dual). If you would be lucky, this CPU could unlock to AII/PII x3 or x4 althrough you would need to get new cooling, at least stock cooling from normal PII X4(if going for lowest price as people often throw them away without even testing). I have AII x3 myself that unlocks into "normal" PII with 4 cores and L3 cache, but that's a lottery and your AII can stay AII if you are unlucky or get 1-2 unstable cores;]. Ability to OC is also a lottery, my 3ghz goes on stock voltage to 3.5ghz pretty easily and I simply never had a reason to try higher yet as I even underclock my cpu for my needs instead soo could go higher probably, but that's not a rule, and especially with unlocked cores if they're faulty stock voltage can be not enough for them:]. If you're unlucky buying good cooler will probably cost same as getting better cpu from the start
If that 300W psu is noname or simply old, and have weak 12V output then putting in GPU before replacing it, or even a try to unlock cores could end your build with some fireworks. Good 400 or 450W with strong 12V line and bronze 80 certificate would be more than enough for new PSU, just never buy a noname and don't buy old/used PSU, awfull efficiency and often weak 12V lines, small 12V output, while new systems uses mainly it:].
For GPU some hd5750 would be the cheapest enough to run most modern games at max details above 30fps in HD or HD5670 for a bit smaller res and sometimes medium details.
Depending where you live that $300 limit can be easy or impossible. Prices changes in weeks soo it's wise to wait a bit and try to guess when it'll be cheaper. As an example day after last xmas I ocassionally bought new gpu with 1gb ddr5 memory, 2 weeks later it was 1.5x of it's price for a 512mb ddr3 version. O.o Finding ocassions matters if you really have such limit. Prices aren't too stable currently soo just going to first shop and buying parts will fail
And if you want it badly just for pcsx2 probably getting some nice c2d like e7xxx+ would be better than aII, but getting new one could be hard, which leaves second hand stuff. Generally looking around friends and friends friends for some second hand would be much easier to get into that $300 limit safely(well that safety part depends what people you call friends:]).