I have an 88 Formula 350 and had the same problem. Here's a list of parts that I went through to FINALLY correct the situation: Battery, Battery Cables, Starter, Ignition Switch, and the part on the steering column under the dash that the ignition switch connects to (I think this piece is most likely your problem, cheap and easy to replace or bypass). I also had to replace the Alternator, Drive belt, and soon to be Timing chain and Head gasket. Also I bypassed the Ignition switch and installed a push button starter switch in my center console (everyone thinks it's SO cool, easy to do as well). But i'd check for continuity on that piece under the dash...I believe its the yellow wire that should have power at all times...possibly red.
