Engine starter not working?

It starts at 12.54 when I turn key it drops go 5.7.

The car will experience a NO start condition. When the ignition key is turned the starter will not engage. However, after removing the baterry cables for a few seconds and re-installing them the car will start normally. It will then work for several starts, but then will repeat the same condition. The battery is new and the cables are clean. What could be causing this issue?

It will not start and the anti theft lock light is on. Tried
unhooking and rehooking battery, lock and unlock door, jumped the battery. What's up?

See below

Your PAT (Passive Anti Theft) system has put your car on lock down. The only way to get past this is to get it to the dealer. They have a special program that will unlock it for you. A lot of the time when you unhook the battery, especially in newer cars, they tend of freak out. Kind of like having to put in a radio code when you change a battery, only worse. Should be a quick fix though.

My vehical after a full day of driving wouldn't start last night. When I put the key into the ingnition and turn all the way forward the motor won't turn over. Sometimes the radio and interior lights will come on.

Turn key all the way - all dash lights come on, car has power (radio, windows, etc.) - But car does not start. Does not crank, etc. Nothing. Tried both keys in case it was the key. Won't start. Played around with it for about 20 minutes, car suddenly starts when key is turned like nothing ever happened. Car runs fine for 3 weeks. One day - car will not start again. Mechanic plays around with it for 20 minutes, everything has power, car will not start. All of a sudden - car is fine.

About 2 months ago the engine was stalling out on a roadtrip. Assumed it was the fuel pump. Replaced it. Over the weekend it happened again. Plugged it into my OBD2, and it said I had a bad fuel rail pressure sensor. I have one on order. Now tonight we were leaving my sister's, about 6 blocks away we were sitting at a very long light. Just as it turned green, the truck stalled and wouldn't start again. By not starting I mean, no crank. I pushed it into a parking lot, put cables on it, assuming my new battery died. Checked with a meter, had well over 14v while connect and even 12.9 after. Still nothing. Signs would point to a starter if I had shut it off, but the truck stalled and died. I didn't have a lot of time to spend with it before my sister showed up with tow straps and drove us home. I am a pretty avid mechanic. I've never seen anything like this. It's not even trying to put power to the starter, because the lights wont try and dim while turning the key. It is also making a weird buzzing sound in the radiator area with the ignition key in the on position. Noticed that when I was hooking the straps. Never heard that before, and I have been under the hood of this thing for years. Looked at the anti theft light also, it wasn't flashing with the key in the start position either. This is a new one to me, and can't find any threads or videos either.

It isn't a voltage issue. 12.9 is as it sits. Again nothing dims as you try and crank. Something is telling the starter not to engage.

I really didn't pay much attention to the security light. And yes, I tried both keys. I do have a volt meter. I haven't had a chance to try testing everything yet. I am going over after work this evening with all my tools and meters. Also see if anything scans on the OBD2.
However I feel the stall and no crank are related.
Also I had the PCM rebuilt a few months ago. By a reputable company, replaced all coils and plugs.

When I turn the key on the engine will not crank because the shift indicator square does not appear on the P for park. I have changed the shift indicator/position sensor and the ignition switch but still does not work.

Yes, that image is the PCM which I had rebuilt a couple months ago.