Q: My car won't consistently start?

This has happened only once before about two weeks ago and eventually the car started. Today I started my car, drove it to the store and everything was fine. When I got back and tried to start it, the engine did not run. The lights, radio, air, etc. all turned on. There was a faint whirring noise, but no clicking or engine cranking or any other sounds. I tried to start it several times in park, neutral, with/without braking, etc. but nothing worked and eventually the brakes got really hard to press. I sat there for about 30-40 minutes trying to look up stuff online and I think (and this may not be it at all) it has something to do with my car not going fully into park. Eventually after the 30 minutes or so, I tried again (having done nothing) and the car started up perfectly fine. I drove home, turned everything off, and then tried once more (hoping it was a fluke) and the car did not start. What is going on with my car? Is there a simple fix or do I need to take it to the shop? Help??

My car has 186000 miles.
My car's transmission is unknown to me.