HD3650 don't support openCL but they do support Stream, odds are your Pyrit is going into Stream mode and not open CL. 

The entire 3xxx family has no OpenCL support, sadly the SDK tends to report it as a valid device, until you try to go use it.

Since you're limiting yourself to $100, your best option I guess is to try to get a 5830 but you would be better off trying to come up with the difference and getting yourself into a 5850+.