What would cause an intermittent no crank no start? 2002 Impala LS

I have a 2002 Chevy Impala LS 3.8 that on occasion will not start. I turn key to start and nothing. It does not click though. I turned the key to ACC and get power in car (lights, gauges, etc.) then proceed and turn to RUN and still same. Then I turn to START and all power goes away and will not start. Once I let go of the key or turn off the key the power all returns. After like roughly 10 minutes give or take it starts. I have been told so many different things and don't want to just start throwing parts at it and wasting money. Some say starter, ignition switch, alternator, bad connection (ground, power, etc., passlock sensor, and some say it may be the aftermarket remote start the I had installed. I took it back to the place and they said it had nothing to do with what they did but couldn't figure it out. I had a starting/charging system test done and nothing. I had someone check the ignition switch and he said it seemed fine. A little more detail that may or may not be relevant, not too long after having remote start installed, they had to replace the BCM they installed because I was having issues with the door locks not unlocking when disarming the alarm. I did however have another couple times since where the locks did not unlock. I know this is a lot but I am trying to give as much detail as possible to help narrow it down. Oh and the battery cables are tight at the terminals.