Car randomly doesn't start

Hi, my L300 has a few issues, but the most problematic at this point is that it won't start. Some days it will, some days it won't. And jyou can't jump it off. It sounds like it's cranking and starts to catch but then doesn't. I had a problem like this with my lawnmower, and it was bad gas. But this car doesn't have bad gas, I don't think. When it will start, it runs as it always does. We had it to the dealer, and they think it's the BCM because of some other issues that I have with it, such as the door locks sporadically not working, the radio sporadically not working, etc. It is not throwing any codes. Another mechanic doesn't think the BCM would cause it not to start and that it may be the ECM. Yet another thinks that it might simply be a faulty ignition and a very simple fix. The other thing that it has done for a few years now is that it has what I would call a performance issue. In low cruise speed, such as in a neighborhood, the car kind of sporadically loses power (not one big drop and engine boggle) just sort of like misfiring, but that's not it exactly either. It you stomp the gas, it will go. And every rare now and then I smell unburned fuel. But no one can tell me what is causing this. The transmission was just fully redone because it was shifting hard, and this is fine now. I really want to sell this car, but I can't in good conscience sell it when I know it's going to be a headache for someone to fix! Can you help? The fuel filter is good, the throttle body control module and gas tank were replaced a couple of years ago becuase I was smelling a lot of unburned fuel, and they told me I had a tank leak. But right after that, maybe, is when the performance issue started. Thanks for listening. I'm frustrated.
Kyra