2006 TL No Start
 

P0118, P0113, P0406, P2628, P2631
[Cleaned and tested EGR valve]
This is what I've been dealing with this past 2 weeks or so,
No indicators of anything going wrong. Drove it one day parked it was perfectly normal, next morning does not start and key wont come out (anti theft light comes only after trying to remove). Bought a new battery after not knowing how to remove my key and drained it.(while disconnecting the negative terminal, the key then comes out). With the new battery same thing happened. But NOW the D5 light is blinking with a check engine light(and the codes). I've checked all fuses. and tested the starter and ignition relays. On top of all this sometimes when I'm working on it, it will start. Little bit harder of a shift when going into reverse but everything runs fine. And if I'm lucky I can turn it off, pull my key out, and start it again. But only a few times until my key is stuck again.

I'm going to test my starter. I also read that I should take a look at my neutral safety switch. But I guess what I'm asking is why would 4 sensors go out all at once and no fuses are blown and ultimately what will get this car started again if you had to guess from the info given. Just don't want to go replacing things I don't need.
Let me know.