Starting issues

You are thinking on the right track. Very first thing I'd do is to determine if you have a "draw" and then go through the cables and starter relay

To check for a draw, get the car parked, everything "off." Check things like dome light, trunk light if equipped, etc.

Remove the battery ground cable, and put a 12V test lamp in series to complete the circuit. This is best done in subdued lighting. You should see NO lamp glow at all.

If no lamp glow, or maybe a dim glow, take your multimeter and carefully set it up for the high current scale. You must be careful, as a meter current scale goes in SERIES, and too-high current can damage some meters, or pop an internal fuse. Put the meter in the ground cable in place of the lamp. Decrease the current scale setting, looking for any current flow indication. Should not be more than "just a few" milliamps

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If this checks out, "normal" everything up, reconnect. First though, CLEAN the battery posts and clamps with a real -by - george battery post cleaner, and tighten them up. Retry the start

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Now let's make some checks. On any Mopar in these years, all use a starter relay which does two things.......

A....relieves the ignition switch of high current draw to operate the solenoid...

B....provides the component for the strategy Ma used for the neutral safety / clutch safety switches.
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You will have a starter relay, looks like this:



the big stud is a battery junction point as well as one relay contact. It is ALWAYS hot to the battery

The "square" screw terminal is the other contact and runs down to the starter solenoid

The two "push on" terminals are electrically interchangeable, and hook to the relay magnetic coil.

One terminal goes to ground through the neutral safety or clutch safety switch

The last terminal gets power "in start" from the key

ON YOUR CAR THIS WIRE may be interrupted by the SEAT BELT INTERLOCK. This is a GREAT time to bypass it and get rid of what might be a problem

Read this:

bypassing interlock system

Won't crank

Nuetral Safety

The short story is the box with the reset button, under the hood, has two "yellowish" wires. Splice those wires permanently together.

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To check out the start relay, first thing is you need a good hot battery and good cables and connections.

If the engine will not crank, hold the key into "start" and wiggle the shifter from park to neutral and back, listen for cranking or clicking

If that does nothing, identify the wire coming from the relay, from the "push on" terminal, which goes down the firewall to the transmission. One wire goes to the bulkhead connector, the other goes down to the transmission.

Pull this wire loose, and ground that relay terminal with an alligator clip lead. Be careful the transmission is not in gear, and try the key. It should crank. If so, there's problems in the neutral safety switch

If the relay clickety clicks or buzzes, this is low voltage.....concentrate on a dead or bad battery or bad cables and connections.

Hook your meter to the battery posts and hold the key to start. Does the relay click and buzz? What does the meter do? If the battery voltage is above 10.5V then you have cable problems

Post back results and we'll go on from here
Great info. I will try all that and let you know. Thanks.