Thanks guys. I'll definitely check the flapper, Wristy. Seems like a good place to start anyway.
It is cranking fine, no problems there. Leftcoast, what I meant by catching was that it would fire once, not that the starter was missing. My old '79 F150 had a missing tooth on the flywheel. . .not my problem anymore.
I thought about the fuel pump and filter. . .I guess I don't understand why starter fluid or a push start is any different than cranking in this case.