You need a cable that connects from your car to your computer. They used to be around $40 maybe even less but they are close to $90 if not more. And if your any good at soldering/electrical work you can make one yourself.
http://www.plmsdevelopments.com/images_ ... f_rev4.pdf
ECU Talk is free and can check the codes on your car.
Or if you know how to take interior panels apart you can take the passenger side (right) kick panel off and unscrew the ECU (2-3 screws) and follow the instuctions in the service manual. Hopefully you still have the one that came with your car, if not its on this website.
Honestly though find anything (no matter how small) thats wrong with the car and post it here. These cars were not meant for some people like us. These cars are for doctors, lawyers and anyone that had more money than they new what to do with.
Trust me don't waste your time finding shops that check codes on a Q, never mind work on one (And actually fix it). Unless you find a 300ZX shop, Nissan/Nissan Infiniti specialist or a Senior Infiniti Tech on a Friday just before the shop closes your better off with the two above methods.