Or start saving?
With a budget of only $300 ... honestly, you're not going to get a machine capable of playing higher-end games like Dishonored, Bioshock, and so on.
Let's break this down, and I'll try to be as frugal as I can.
Maybe I can find parts that wuld let you squeeze in under $400. I'll honestly try; I'd love to surprise myself and succeed!
VIDEO:
http://www.newegg.com/Product/Produc...82E16814150659 $45
... XFX is a good brand. The HD 5450 is older, and not the top-shelf card of it's generation either, but it'll suffice for most games like those you list on low-medium to medium graphics.
PROCESSOR:
http://www.newegg.com/Product/Produc...82E16819115078 $120
... the Intel Core i3 is still a good CPU, dual-core at 3.1GHz isn't going to set speed records, but it should do what you need.
MOTHERBOARD:
http://www.newegg.com/Product/Produc...82E16813157302 $75
... you have to have one with an LG 1155 socket, that's what that CPU fits. This is the cheapest one on NewEgg that has a brandname I recognise as "not garbage".
You'll notice, we're already at $240 ... and we still need a case, a power supply, RAM, a hard drive,
and an optical drive - bare minimum.
RAM:
http://www.newegg.com/Product/Produc...82E16820139770 $38 ... 4GB (2x2GB)
... Kingston is a good brand, they make reliable memory. Since this is only 2 sticks, and the motherboard Ipicked out has 4 slots, there's room for inexpensive expansion later.
HARD DRIVE:
http://www.newegg.com/Product/Produc...82E16822236271 $72 ... 250GB
... WD is one of _the_ names for quality PC hard drives (Seagate is the other). This is about as small and inexpensive as WD drives come.
POWER SUPPLY:
http://www.newegg.com/Product/Produc...82E16817256071 $70
... Silverstone is a reasonable brand, and "80+ certified" helps ensure it's not
complete garbage. I'm not sure you'll even need 600W, but you definitely
won't need more.
OPTICAL DRIVE:
http://www.newegg.com/Product/Produc...irtualParent=1 $19
... Lite-On is pretty standard stuff. This one is good for DVDs and CDs, but can only read, not burn.
CASE:
http://www.newegg.com/Product/Produc...82E16811133094 $45
... Thermaltake is a good case manufacturor. However, this case only comes with 1 fan, you should really have at least 1 or 2 more. I'll get to that later.
EXTRA FANS:
http://www.newegg.com/Product/Produc...82E16835103052 $14
... CoolerMaster is a reliable brand, and this pack - about the price of 2.5 to 3 fans - gives you four of them. One or two for the computer, the rest as spares (fans do wear out, after all).
...
FINAL TOTAL ... $493 ... and you'd have to put it all together yourself. And you have to re-use your current Keyboard, Monitor, Mouse, and Speakers. That doesn't include Shipping and Handling on the parts, either - but OTOH there might be a few rebates and such I didn't bother paying attention to.
Sorry. I
did try ... but I'm just not willing to recommend
garbage generic-brand parts. If it's not something I'd consider for myself, in terms of
quality ... it's not something I'll suggest to someone else.
Still, I know you say $500 is impossible for you ... but, at least it's got to be more possible than $1,500 ... right? And, all those parts are
currently in stock, too.
"Can run games well" is what "gaming computer" means.
It doesn't have to be the bleeding-edge-est supermachine to be a gaming computer.
What it needs to have is ... well, the list above is a pretty good "start here" point. Anything less, and you will be stuck playing "PopCap" style games,
not Dishonored, Bioshock, and so on.