Will start two times in a row, then refuse to start again

Ran into this last night. Tried starting the car and nothing occurs; no crank no start. I hear the fuel pump in the back, but when I turn the key to start position, nothing happens as quiet as a cricket.

I let it sit for a few hours. Tried it again, nothing. Let it sit for a few more hours and tried it again. It started. Let it run then turned it off again. Tried starting again and it worked. Turned it off, and it would not start, no crank no start.

Tried this morning and it started the first time. Second time too. Third time, nothing again.

Background: 1997 Ford Taurus 3.0L V6 engine. Previously had issues with the additional gear for overdrive. It kept the 'check engine' light on. Then about a week ago, the transmission began going into 'limp mode'. If I attempted to accelerate too quickly, it would not come out of first gear no matter how high the rpm's went. One time had to let it sit for a few minutes, turning it off and on and finally it would go to the next gear. The second time it happened, I had to drive around a little bit in first gear to get it to shift up. Then the check engine light went off and the car began to sound like a diesel with that diesel car sound on the mid passenger side under the hood. Then, it simply is being stubborn and refusing to start now.

Confirmed fuel pump off switch is not triggered. Battery has a date of 04/16 on it. But if it is the battery, why would it start a few times, then refuse to do it?

Possibly thinking its a TRS (transmission range sensor) due to the limp mode, but not sure about that. Fuses all looked good, tried spare key. Only hesitation on it being the TRS is that it will not start in Park nor Reverse nor Neutral nor Drive (I had the parking brake engaged to ensure I didn't go flying if it did start).

Only thing I notice is that when it refuses to start, the front headlights will go out when I am attempting to start it, but dash and interior lights are fine.

Further background; due to flooding, I did have to drive through some rather large 'puddles'. Occasionally after these, I would lose all power steering control for a few seconds. I resolved that issue when I would go through these by turning off any interior ventilation I had going.

Any help or things I could try would be great.