This is my current graphics card on my laptop. I'm having a very difficult time trying to get GPU mining to work with this.

Ive installed the latest catalyst as well as the ATI APP SDK, and when I open GPU Caps it still won't read my GPU as a device.

It seems like my graphics card isn't supported by OpenCL?

I'm pretty new to all of this so any help would be greatly appreciated.

Here is a good reference: https://en.bitcoin.it/wiki/Mining_hardware_comparison

Just out of curiosity, which 4300 card do you have? The above referenced page seems to indicate that a 4350 can get just under 7 mhash/sec.