If it's the usual Mopar ECU set up I think the coil primary should be about 1.7 ohms, not 3 - 4.
The ECU in the pic looks too new to be five pin. If it is 4 pin then whoever wired it up with a double ballast likely didn't fully know what was what. So I think you may want to start from scratch to be sure you have it all correct. Then you can lose a few of those wires.
So first unplug the ECU and check it's got only 4 pins on the module. To diagnose the ECU connections you just need to understand and check what each of the four wires is (should be) doing (since your problem is ballast related you might like to skip checking the ECU 'til later and check the coil connection first - see below) but while you're in there better to check it all out.
If the ECU plug has five wires don't worry, it will be obvious from the position of the "missing" pin which wire is doing nothing (as CP says it should be the green with a red trace). But remember, on a 4 pin ECU there are still five connections, the 5th one being ground to the casing.
So on the plug you should have 4 (active) wires - this is what they do:
2 of the wires are from the pick-up coil in the distributor. They do not connect to anything else at all (you can get them to run with these swapped over but there is a "right way round" which runs better);
1 wire is a basic 12v supply (this is power supply to the ECU and nothing to do with power to the coil, so it should always be a straight 12v except when the ignition is off when it will be zero, it doesn't go through the ballast at any time - the ballast has nothing to do with the ECU on a 4 pin system);
1 wire goes to the -ve side of the coil (this is what the ECU switches to ground to energise and de-energise the coil).
You can easy find a wiring diagram on here somewhere to see which is meant to be which, but make sure you know what you are looking at - it's quite easy to see a picture of the socket and accidentally think you're looking at the plug - they are of course the reverse of one another.
Now you can see if what you've got is what it should be. Unplug the distributor connection (on the stock wiring there's a little connector that can only go one way) and you can just check those two wires match up correctly with the ones in the ECU plug using a test light or something, same applies to the coil -ve wire (disconnect it first so you don't see a false result from anything else).
Checking if you have a constant +12v at the ECU is not so simple, but at least it's easy to check you have some kind of +ve feed with the key on run and on start (if the car starts and runs at all then there must be at least something there, they will run even if this is connected through the ballast, I know because I tried it - it would run fine and then stall at idle if I switched on the lights - LOL).
Then the last piece of the jigsaw is the +ve connection to the coil. With the key on start it should be direct and on run it goes through the ballast first.
Basically there is a +12v wire from the ignition switch that goes to the coil side of the ballast when you turn to "start" and another wire that goes to the other side of the ballast when you are either on "run" or on "start". On stock systems they are blue and brown. With these wires disconnected from the ballast you can use a simple test light to check they are going live at the right time.
Now you can understand what's going on with all these connections and you will also understand why the wire to the the coil side of the ballast is continuous with the +ve side of the coil and the wire to the other side of the ballast is continuous with the 12v pin at the ECU.
As a diagnostic aid you can wire things up separately, for example, you can disconnect the +ve side of the coil and just run a separate temporary wire straight to it from a definite +ve supply (like the battery) and fire her up - you'll still need the key on "run" to power the ECU, and turning off the key should still shut it down, but be ready to pull off the temporary wire just in case it doesn't !. And don't leave it running like that more than a minute or two or things will start to get hot.
BTW - standard bullet connectors will fit nicely with the ECU pins for testing purposes.
And don't forget the ECU has to be grounded - when I was playing with mine I had it clamped to a stud on the engine.
