One of the first steps, as long as everything else seems normal, is to replace the ignition switch. These are pone to issues in our year group of GM vehicles. GM revised the switch a few years ago, the part number you seek is a ACDelco D1426D. Buying an original GM or ACDelco is really in your best interest, and make sure it has a gray cover over one side, the original had a complete black case and has issues.
Supercharger installations on the Chevy SSR require a higher pressure fuel pump for proper operation. To allow the factory fuel pump to operate a supercharged motor there is a fuel pressure booster interface box installed that makes the factory fuel pressure pump operate at higher pressures. During installation of this aftermarket part, it is noted that after time, either the fuel pump fails, of the booster box or wiring can have issues. A common problem is for the gray wire at the fuel pump booster (usually mounted on the factory fuse box) begins to char due to a loose connection.
Check the gray wire at the fuel bump booster for discoloration and repair as necessary. Check the splice on the yellow wire for proper security, and insure that the fuel system has 60 PSI at the rails.
Here is a link to the Magna Charger installation for the Magnavolt fuel pump booster on the SSR. http://www.superchargersonline.com/installmanuals/magnacharger/manual-fuelpumpbooster.pdf