1990 Corolla Commonly Won't Restart

#1
Wondering if anyone can solve this problem.

I have recently acquired a 1990 Toyota Corolla 4wd wagon with the 1.6L 4AFE engine. Commonly I am finding the car won't restart after being shut down - I have had to tow start it several times now. It will crank fine but just won't fire up. Also once running the engine dies or hesitates on acceleration. Other days it starts and runs fine. Anyone else had and solved a such a problem?
 
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