Ok with a bit of scrimping messing about you should be able to get a 7950 or gtx 670 mATX mini tower with 8 gig of ram that will be reasonably quiet. Gonna be a cheap ugly case though,
here's a part picker site http://pcpartpicker.com/
or you can use the rig builder on this site.
AMD 8320 to start. They've got the power of an i5 for around $140 Also comparable MoBos are less expensive for AMD
coolermaster hyper 212 evos are very quiet, can handle the chip, and are $30 You want to add $5-10 you got a lot more choices.
miniATX will make things cheaper, but you get only one video card slot so less futureproofing.
Have you considered also scavenging your old case? or is it some Dell prebuilt with all proprietary garbage inside? Also, how much HD do you got? You may want to add a games drive.
I tried to just stick one together, but it would be a system I liked rather than one you liked.
Try and keep the memory tight. Memory with CAS over 9 will start to get slow on you. How hard do you want to overclock this thing? Water is mostly out at these prices. The 8320 basically requires some overclocking.Edited by bombastinator - 10/4/13 at 5:29pm