That ram is DDR2, so if you decide to keep it, that is going to present some challenges in terms of what motherboard to use. $300 is a tiny upgrade budget for a motherboard, PSU, CPU and a decent case. Your old CPU isn't worth salvaging, and finding a socket 775 motherboard that is an upgrade over what you already have isn't very easy these days as most of them are being discontinued. Here's what I would do in your situation.
Case: Cooler master CM 690 version 1 ($69) http://www.newegg.com/Product/Product.aspx?Item=N82E16811119137
Plenty of room, good airflow, well made.
PSU; Antec 650 watt ($65 after rebate) http://www.newegg.com/Product/Product.aspx?Item=N82E16817371015
should run what you have adequatly, would want to go bigger if you ever plan to do SLI.
Motherboard: Asus P7H55-M motherboard Socket 1156($89) http://www.newegg.com/Product/Product.aspx?Item=N82E16813131623
It's a small form factor board, but it will get the job done. 4 ram slots, decent chipset. Requires DDR3 ram
Processor: Intel Core i3 530 2.93 Ghz Dual Core Socket 1156($114) http://www.newegg.com/Product/Product.aspx?Item=N82E16819115222
Realistically you want one of the quad core or core I7 chips. but we're on a budget.
Ram: G-skil DDR3 2GB sticks ($37 each X 2) = $74 http://www.newegg.com/Product/Product.aspx?Item=N82E16820231393
That would get you back to 4GB, buy an additional 4Gb when funds permit for use with windows 7 64 bit. Usually I don't use G-skill, but again, we're on a budget...
So, that would put you at $411. If you can find a free usable case somewhere, that would put you around $300-ish.
You may also want to think about picking up a new SATA hard drive at the same time, just because of the fact that hard drives age and will fail eventually. 5 years is about average lifespan for most drives, and I would suspect you are getting near that with that machine. Should be able to find a decent Western Digital one for around $35. Aslo a Sata 22X DVD burner for $30 would speed up game installation considerably. Those could always be added later though.