Hey, im new to the whole rotary area so I was wondering if you guys could help me out. I just bought an 88' 7. Didn't really have an interior but the engine started. Only problem then was the clutch was broken. Now that i have it back at my house I can get it to start but as soon as it starts it cuts out. My friend was lookin at it and he says it could possibly be a problem with the fuel pump. Like im not getting any compression. Any other ideas?

 

It could be a problem with the AFM. It is not used until the car runs for the first few seconds.

 

The first thing to check is the idle settings. Rule them in or out by propping the throttle open a little when starting, or have someone press the gas pedal. If it runs, then you now know where to look for the problem.

If it still dies, check fuel pressure, spark & test the Air Flow Meter like jwc3299 suggested. The factory service manual or a hanes manual can help you with that. You can find the FSM here (http://mazdarx7.iougs.com/), along with other helpful NA info.