iPod tells me to log in to iTunes account on a computer. What next?
You are doing everything right. Sometimes an error on the other end (apple's servers) can look like a local problem to iTunes. Most of the time, what you did would have fixed this.

Have you considered getting a hand from the billing / account people that work for Apple? Start with the Account &amp; Billing section on the left...

Your computer needs the OK from Apple's on line servers to fix the errors. This is an account issue and you don't have to pay for this support (but may have to start by emailing apple if no one is free when you ask for help). 

You could try authorizing your account on any iOS device or another computer to rule out problems with your online account as well. 

If you get errors on your computer after you re-authorize, you might have to go through this article on iTunes repeatedly prompts to authorize computer to fix things. If the iPod is giving the error, be sure to restore the iPod (which will wipe everything that's not backed up) to get the new authorization to take on the iPod.