I was in your situation a very long time ago and had to get rid of a 21 year old car.
I only buy new vehicles now that come with all new parts and a warranty.
Start here.
http://www.nicoclub.com/FSM/G35/Coupe/2003/gw.pdf
You can obtain a cheap multimeter for testing at Harbor Freight
Don't automatically assume the motor is defective without proving and testing.
Could be a fuse, a poor connection, or a missing ground or even the motor but you need to either do the troubleshooting yourself or pay a professional to do it.
Knowing and becoming friendly with an Infiniti Service Manager and their top fully trained technician that does electrical troubleshooting is a big plus. Make some homemade chocolate chip cookies for them if you think that might help you get some troubleshooting assistance.
See page GW 19
Good luck
Telcoman