You cannot use the iGPU and add-on GPU at the same time unless your motherboard's BIOS has a specific setting which allows it.
Such a feature is not common even on new boards.
Either the BIOS automatically disables the iGPU when an add-on GPU is detected, or you have to manually set the desired GPU location in the BIOS. The "one or the other" limitation is required to avoid a hardware and/or driver resources conflict.
The 9500 GT supports more than one monitor anyway so you'll have to overcome your connection issues at the monitor end, even if it means buying another monitor with the required input port that needs no adapter/converter.