This build is very similar to jmsellars1's, but I think he/she went with an OEM CPU so you will need a CPU HSF for that build.
shipping is going to be $19 and a $30 MIR on the build below. Really, there is no way of scaling anything back in either build, we both are slightly over the $370 budget before the MIR. You listed some parts not needed, so is there anything else salvageable from your friend's old computer like the case, or DVD/CD drive? that would save a few $.