Okay, I don't think it's your memory capacity holding you back, but rather your cpu and video card. They barely meet the minimum requirements listed here:
http://www.minecraftwiki.net/wiki/Hardware_requirements
Remember that in many cases, "minimum requirements" are enough to run the game and not have it crash. Getting a playable frame rate at lowest detail settings might take a fair amount more (especially if you're running at 1920x1080 or higher).
The new motherboard and apu you linked look like they will get you to "Recommended", once you get some memory for it. Since you say you're on a super-tight budget, I suggest this one:
http://www.newegg.com/Product/Product.aspx?Item=N82E16820231395