I have had that happen on 3 occasions.

One was a starter solenoid (on the starter) stuck and wouldn't disengage. My Challenger had the ignition switch come apart inside the column and just by bad luck made a connection from the starter wire to the power wire. The third was a Ford, and the relay on the fender got stuck.

[quote] So....Disconnected the from starter to relay...and it would not crank when battery connected. Then....just reconnected it...and did not crank either...and car started and shut off fine. Flaky relay.....?[/ quote]

Could be a starter or relay.

Hope it helps