Is it impossible to GPU mine without OpenCL? I have an Nvidia 7300 GX and want to start mining with it. This card doesn't support OpenCL. Can I still use it for mining? With BitMinter I can only use CPU mining; it doesn't see the Nvidia card.

I am using Linux Ubuntu 11.10 (Oneiric Ocelot) with all extras...
OpenCL allows all graphic cards to be handled in a higher level in a uniform fashion. As all GPU mining software relies on OpenCL, you would need to create your own software to mine on non-OpenCL card. Whereas it is possible, the process would be very complicated and the reward probably wouldn't be worth it (NVIDIA cards aren't good for mining).

So all in all, no, if the graphic card does not support OpenCL, you can't use it to mine.