Where to I begin?
1. Your initial complaint was that you were angry because you called the airport an hour before you showed up, and were told the flight was on time. Then, upon arrival, you were told it was delayed. Do you have any idea how many things can happen in that hour, that affect flight departures? It could have been weather, equipment, ANYTHING.
2. You didn't want to wait around for a different flight at LAX, so you chose to call the service department and they advised you of a later flight through Chicago, but that you would have to overnight in Chicago. I don't understand why you would choose this option over waiting in LAX. That part is unclear, so I won't comment further.
3. You say the person on the phone assured you that United would pay the cost of the hotel stay in Chicago, and directed you to special services. I have no doubt that you complained about the hotel cost, and that she told you to see guest services upon your arrival in Chicago. I do, however, have serious doubts that she 'assured' you that United would pay. I think you are exaggerating to prove a point.
4. The service desk was 'closing' and would not help you. This is frustrating, I agree. Baggage claim could not help and offered you a slip for a discounted room rate. The part about contacting United later does not ring true. If they were going to give you a voucher for a room, they would have done so at that point. United isn't in the business of 'reimbursing' passengers. It sounds to me like she just wanted to get you out of her line and move on to the rest of the people.
5. After arguing with customer service over the hotel room, they offered you a 100.00 future travel voucher. Again, I have no doubt that they offered this to you just to quiet you and move on. Makes me wonder how much the room night was? You don't state this anywhere.
6. You booked an itinerary online, okayed it, read the terms and conditions, and then the computer 'magically' it changes it and sends you a completely different itinerary? Um, no.
7. You state that you are 'done' with United, so what is the purpose of your complaint? What do you expect them do to at this point?