I'm sorry, but this doesn't sound like United's problem. How can you just stand around waiting for your flight to be announced and let the boarding time and departure time both pass by? And then to complain that the agents taking boarding passes for another flight wouldn't talk to you and you somehow made your way to Customer Service at which time they boarded your flight just doesn't make any sense.

You are not owed a refund on your airfare or lost wages no matter that you can produce a contract and receipts. You're missing the point.

Sorry to be snarky about this, but it sounds like you need to find employment closer to home.