I am not able to authorize my new computer, or deauthorize my old one in the account area, even though that should not matter since I can have 5 devices, right? So I cannot buy or rent any movies this evening.
How are you trying to authorise it ? You should be able to do it via the Store drop-down menu at the top of iTunes e.g.
You can have 5 computers authorised at any one time.
Retrieving data ...