Randomly will not start

Intermittent issues with the vehicle's communication network are common on these vehicles and always will leave a code in the power-train control module, but 9 out of 10 technicians cannot properly diagnose this sadly. If you can have the codes retrieved after you have another no start symptom there should be some codes stored in the PCM or SJB, we can help decipher and narrow down the cause.

Yes, even a low voltage issue will set codes in several modules. Your local parts stores usually will retrieve codes from your pcm for free and either get you a printout or just write them down. They may or may not be able to get codes from any other module though.

Depending on the store they may only scan for the common OBD II codes not all of the codes available like from the security modules or other controllers. However random starting like that sounds like a corroded connection in the starting system. It is providing power to the lights and the rest but the starter isn't getting voltage. When it doesn't start, if you have the lights and the rest on, do they do anything like dim or shut off when you attempt to start it? Does their seem to be anything in common with the times it won't start, like just came off a long drive? Outside temperature dropped? Hit a bump?
Have you tried shifting into neutral or shifting into a gear and back to park?
I would also check the starter relay and it's connections in the battery junction box under the hood. I have seen those corrode and cause random issues.

Yeah most parts stores only have very basic scan tools that do not have the capability to read codes from body modules, and this will need to be dealt with at either a dealer or a good independent shop.