1987 Chevrolet Cavalier won't start without cycling the key

1987 Chevy Cavalier RS. Won’t start when the engine is cold unless I cycle the key 3 times (turn to “on,” wait 10 seconds, turn to off, repeat). I replaced the fuel filter, the ignition control module, and the brake booster (it had a vacuum leak that was causing starting issues). None of those did the trick.

Sounds like classic symptoms of a fuel problem . . . quite possibly a weak fuel pump