Can i make a good gaming desktop with a little over $300 us dollars not counting tax in the total?

With that low of a budget there are definitely some sacrifices you have to make.

1) most likely going to have to buy most parts used ( http://reddit.com/...rdwareswap and ebay and craigslist, etc). Definitely have to build it yourself, prebuilt are def out of the question if you really want to play any games at all.

2) you will not be able to really add things in to your budget such as: monitor, headphones/speakers, a gaming mouse/keyboard, or an operating system. (so you will have to use a monitor or tv you already have, use like your phones earbuds or other speakers/headphones, use a very cheap mouse/keyboard, and either pirate windows 7 or use linux or use a already owned OS)

that being said id look for something like this:

CPU: used amd phenom II x4 or other similar older amd cpu. You may also be able to get a core 2 quad for cheap, which are also still decent cpus. (tho a phenom II x4 is better)

motherboard: any used motherboard you can find that supports your cpu. Get cheapest one possible.

ram: 4gb of any used ddr3 ram (unless you get a board/cpu that only supports ddr2)

case: cheapest you can find new or used. (like a $20 case or less)

PSU: try to get a used corsair or evga etc decent quality psu. Like the cx430 or something. I've seen them sell for like $20 used. Don't want to get a cheap/generic psu.

hdd: any used 500GB/1TB hdd.

GPU: what ever money you have left, spend on this. You could probably get something like an amd 7770 for like $35-40 used. That should play modern games on lower settings just fine. And max minecraft easily.

kb/mouse: cheapest you can find. Like $5-10 ones.

Windows operating system is about $85
There may be used desktop PCs around at $300, but they are best bought locally.
At $300, you are looking at laptops that can't be upgraded.
http://www.tigerdirect.com/applications/SearchTools/item-details.asp?EdpNo=9602662&CatId=4935
http://www.bestbuy.com/...Id=2996026
A8-6410 with r5-6410 graphics
It is an Intel core i3-4010U equivalent
Does well on Minecraft depending on all the mods
http://www.game-debate.com/...quirements
plays cs: go
http://www.game-debate.com/...quirements

Acer desktop of normal size
http://www.newegg.com/...6883101068
$332 delivered
A6-6310 is a little slower cpu, and the same graphics
The cpu is motherboard soldered and not very good.
I think they start at about $377
http://www.amazon.com/...00LSRW9GW/
A8-5500 is a decent cpu and OK graphics for those games.