Electrical gremlin. Dart won't start. Desperately seeking insight!

Playing with the shifter until the starter works is a classic sign of a mis-adjusted shift linkage or a bad neutral safety switch (nss) on the side of the tranny. Mis-adjusted is most likely. The factory manual will tell you how to adjust it, or just follow the shaft and look for an adjustable length piece and use common sense. You want the spring detents on the column to match the spring detents in the tranny's valve body.

Since it will also start in "N", you should always be able to move the column shifter around near there to find true "N" in the tranny and get it to start. All the NSS does is ground the wire from the starter relay coil. You can bypass it with a jumper wire, but not smart since it could then start in any gear and the car jump forward or back. A lot of gomers have been pinned to their garage wall fooling with that.