2nd gen 1986 rx7 not firing up
 

Is it all stock? I would do a compression test for starters. Go get a piston engine compression tester. Take out the schrader valve from the end of the hose. Do the test from the bottom plug holes. Have a buddy crank it over while you hold the compression gauge and you should see 3 even bumps on the gauge needle around 90 ish for each rotor. Its very easy to do and gives you a good idea of the engines health. There are lots of vids on youtube about this if you are unsure.

I would also perform a compression test to start. Are the plugs wet or dry after cranking? Ensure you're getting spark from the leading and trailing coils. Any loose or dangling connectors in the engine bay?

Is it flooded?

Remove the EGI fuse, floor the throttle and crank a few times. Put back in fuse, try to start. May have to play with the throttle.