I'm sorry that some of the people that wrote to you in this thread were not very nice to you. They really didn't have the right to be so rude to a child, and as adults, they SHOULD know better.
They do have IDE to SATA adapters, but none of them that I've seen are very good, at the very least they are not good enough to be used every day. The older hard drives are very slow, and the adapter will not improve their speed.
Unfortunately 300 dollars is not enough to build a decent system. You can however for about 600 build a very nice computer to play the games you mentioned.
If you were to build a cheap system, there is a processor called "Fusion", that would be the best bet for a tight budget, but again, you're looking at about 500 for a good one.
CPU + Graphics- $140 http://www.newegg.com/Product/Product.aspx?Item=N82E16819106001
RAM- $47 8GB (4GB*2)http://www.newegg.com/Product/Product.aspx?Item=N82E16820231314
Windows 7 $100- http://www.newegg.com/Product/Product.aspx?Item=N82E16832116986
Hard Drive- $80http://www.newegg.com/Product/Product.aspx?Item=N82E16822136769
Optical drive- $17http://www.newegg.com/Product/Product.aspx?Item=N82E16827106289
Power Supply- $45http://www.newegg.com/Product/Product.aspx?Item=N82E16817371033
Case- $40http://www.newegg.com/Product/Product.aspx?Item=N82E16811147023Total: $535
Building a computer is not very difficult, but even so at your age this is something best done with your parent's help, if they want to take a look at this posting, I will say to them that this would be a very capable computer and a good budget "starter" for a kid.
You mentioned you already have an OS, if its not Windows7, its probably not going to be good enough to be used, which is why Windows7 is included in the price list.