Car will turn over, run for 4-5 seconds, then shut off. I was going to get a fuel pressure guage to see if the pump is working(around 30psi I suppose???)

What else can I check for if its not the fuel system? Would it be the computer?

Can you give us more info on what year your Z is?

Its a 76 280z

Doubtful that the 'computer' is the problem. It's not really a computer per se like in a modern car but just a control unit. Regardless of what you hear they rarely fail unless they've been abused. Sounds like you need to familiarize yourself with the 'Engine Fuel' section of the Factory Service Manual. That way you'll understand a little more about the car and ask more informed questions which will lead to better answers. You can find a copy of it here:

http://www.xenons30.com/files/FSM/76_datsun_280z.zip