Recently just bought an 88' FC non-turbo, which has no compression in rear rotor (or so told) and has a fuel cut off switch.

Issue is that right after cranking and catching the moment with the fuel on, the car will start but it won't hold idle and immediately die if I don't keep on the throttle above 1k.

Any leads? The motor will be coming out regardless so...

Thanks!

 

Should also mention that the battery drained quickly shortly after attempts to starting it.

 

Well if you have no compression on the rear rotor, there's your problem.

Perform a quick and dirty compression test: http://www.aaroncake.net/rx-7/blown.htm

But it is possible that the rear rotor is fine, and there is another problem. A dead primary injector on the rear, for example, would make most people assume the engine is blown.

Uh, fuel tank full as well?