This article is from the Chrysler-Plymouth-Dodge FAQ, by Dr. David Zatz with numerous contributions by others.
Check the ballast resistor. It's a little white block attached to the
metal between the engine and the driver, with a single bolt; wires plug
into each side. It's easy to replace and under $5.
If the starter makes a rapid clicking noise, your battery may be worn, even if
you can see your headlights.
If the engine was wet, dry it, separate the wires, and try again, Use
silicone spray or "wire drier" or, better yet, replace your wires with
really good ones ($25-40 mail order). These will probably improve your gas
mileage and power as well.
Dan Stern adds: Whitaker's Multi-Mag comes in the same colors and
insulation materials as original, but uses the spiral-wound
construction that you find in wires such as Accel and Jacobs. Lower
resistance, but no irritating radio noise. They have a lifetime guarantee
and don't cost more than regular carbon-string type wires. The
Slant-6 wire set (32605 for pre-75) has the correct 1-piece moulded
plug boots. They are also sold under the Borg Warner/BWD KoolWire name.