How do I transfer a domain I originally registered through Hostony to a new registrar? I've done everything on that end, I just need an authorization number from here. I submitted a ticket and it got passed on to another department. This should be an easy question, so I don't know why it was passed on. Do you have a link or instructions somewhere about how I should request an authorization number from you?

The matter is that the ticket was no doubt passed to the billing department as they are to check whether they can send you the auth code for free or you are trying to transfer a "free" domain. If the payment is ok - you'll get the code very soon, if there are some misunderstandings - well, then your cc will be charged(a free domain registered less than a year ago) for the domain.
Also, the billing department is not available 24/7, that is why you may think that they are slow to respond. I asume in the next couple of hours you will get an update to your ticket request.

Yeah, HOSTONY actually makes it pretty easy to transfer out a domain... Unless it's expired.