I had these symptoms and here's what I did to fix it:
-Re-seated the BMC connections (Didn't fix it)
-Disconnected, sanded and re-seated stock grounds (Didn't fix it)
-*Simultaneously replaced my batt & alt due to lack of starting voltage & alt high-pitch squeal + upgraded/added beefier power & grounds to/from body+motor+frame+alt(Big 4) - Fixed.
I recommend first using a voltmeter to test your battery voltage during engine start using the min/max function, also test the charging voltage of your alternator. Replace your batt or alt (as needed) but certainly upgrade factory wiring.. your symptoms are indeed typical of a poor ground circuit or faulty BCM