Excess resistance with positive battery cable on causing no start

Been dealing with what I assume is an electrical problem in my 1968 cougar 302 base. Car was running good. Decided to put new headlights in it and after about 10 minutes the headlights went out and it started running rough. Then stopped running all together. It will crank and act like it wants to fire over but won’t stay running. I had replaced the battery, carb, ignition coil, and points. Also checked for voltage at the ignition coil both cranking and with key on and both seem good(6 volts with key on and 10-11 cranking). Decided to test the resistance between the distributor base plate and my battery negative and I have 50 ohms which clearly is a problem but if I remove the battery positive and test it it’s back to normal at .3 ohms. Does anyone have any insight as to what could be causing this problem?

Current is flowing somewhere with battery connected and throwing off your ohm meter. The 0.3 ohms with pos battery terminal disconnected is the valid test. So no problem there. Any electrical modifications for the new headlights? Assume battery voltage is ok?

No aftermarket anything. I’m rebuilding this car and everything was running good so I decided to get the headlights working so I just threw some stock bulbs in and that seemed to be where my problems started. I’ve put 2 new batteries in and for one of them it ran good for 20 seconds and then stopped and now it won’t run again check the battery charge and it says it’s fine so I’m not sure what’s going on at this point

There is a circuit breaker in the headlight switch that could have shut off the headlights. It should reset itself when it cools off.

The fact that the ohms from distributor to battery are so affected by current makes me suspect block might not be well grounded to chassis. Make sure all battery cable and ground connections are tight and clean. I believe the 68’s used a ground strap from block to firewall? So make sure that’s in place.

There could be multiple problems, too. When mine mysteriously stopped running like that, it was sediment in the fuel tank that kept plugging my carburetor.

Just throwing out some random ideas….

Did you put halogen headlights in? Halogens will draw more current, and can trip the circuit breaker.
Check out WCCC item 30086 for conversion to halogens.

Performing a voltage drop test between the negative post and the block is the best way to test the ground cable. This test should be performed during crank and not exceed 200mv. The same test is valid for the positive cable.

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You may wish to validate that there was NOT bizarre timing of a different (new) failure coincident with your new lights. I recommend you disconnect both headlights and see if all is well (in other words it goes back to running like before). Reconnect and then validate that the problem returns. If yes, check each light’s connections to ensure you don’t have shorts or oddball grounding issues. Go from there.