Unable to log in to iTunes

Question

I have been using the same username for my iTunes for years.  I use it on iCloud, the App Store...everything.  About a year ago, I completed an iTunes update on my Toshiba Satellite laptop and was unable to listen to any music on my iTunes after that.  Nothing would play.  I followed some "advice" on the Apple Support Communities since it was clearly an issue several people had.  The advice had quite a lengthy process which included eventually removing iTunes and reinstalling it.  I did the process step by step (which supposedly worked for others), and I was never able to log in to iTunes again.  My iPhone music still worked since I hadn't logged out of iTunes, as did my iPod (Nano, Classic, and my new Nano) since you don't log out of those.  I have since logged out of iTunes on my iPhone and I was never able to log back in and it shows that I have no music because it claims I do not have an account (though I can log in to the iCloud or App Store with my account).
I also have a MacBook Air and an iPad Mini.  I never used my iTunes on the MacBook Air, so I have tried logging in there, and have also tried "approving" this computer for iTunes use but still...I can log into iCloud, the App Store, and have verified my account on the Apple support page (http://www.apple.com/support/appleid/) but I still get the following error:  
I still am logged in to my iTunes on my iPad though I know if I log out, I will never be able to log in again.  It does not have all of my music on it...just some of it.  My Classic has all of my music, and my old Nano has since died.  I never got to load anything onto my new Nano.  So, I opened up a ticket with Apple and of course there was the big runaround saying I had to pay for service on my MacBook Air since it's a problem with my MacBook Air, but after much arguing, I got it through their head that it's a problem with my Toshiba, Macbook Air, iPhone, and will be with my iPad as well if I logged out of iTunes.  They finally opened a ticket and had me to talk to several people.  The last person to work on it at Apple stated she was sending it to an engineer, because even she tried logging in with the same username and password and was unable to, though she was able to log into my iCloud.  She "remoted" in to my MacBook, and could not find anything wrong either.  The last I heard from them was in June 2014 where they told me they were moving this to an engineer (after 3-hours of being on the line with them) and stated that I would receive a call back, which of course never happened.  I have called that person back several times since she had given me her extension, and she does not return my calls.  In the meantime, I have tried several times to just change my password on the account, and it changes my password on every account but I still am unable to log in to my iTunes. 
Here are the notes I took while on the phone with them:
June 2014:
Case ID: 619383300
xxx (can't remember his name...maybe Scott???  Transferred to Tim)
Tim (iTunes. Can't see an iTunes problem. Believes this is a computer problem)
Eric (did the sharing session. He's with "mac problems".  Immediately said I would have to get a warranty for my computer in order to receive support. I refused since I was not going to warranty my iPhone, Macbook Air, Toshiba PC, and iPad just because of an iTunes problem).  He later stated this is a problem with my internet provider, because of the blocks i have set up for my children.  I do not have blocks set up, never have, and it can't be an ISP problem because it would be an ISP problem with my UK internet, US internet, sisters, brothers, and parents ISP's as well since I have used their internet and still cannot access iTunes. Sending back to iTunes)
Tay (iTunes Senior advisor. Sharing session. Checked Apple ID while remoted in to my computer.  Cannot see any problems.  Sending up to Engineer. Sending me a case number and personal contact number.)  I never heard back, though I was told by Tay that an engineer would contact me regarding this issue. 
iTunes started a new case ID: 669806831 dated Sept 27, 2014         
28 Sept: Received an email from Anand at Apple iTunes support which told me to contact Apple Support at http://support.apple.com/kb/HE57 to get a phone number to call in and pay for support on my device, though it's not a device issue which has already been acknowledged previously.  iTunes support will not help me so I contacted Apple support.  They say this is an iTunes problem, not an Apple problem.  iTunes says this is an Apple problem, not an iTunes problem.
29 Sept: Left a message with Tay who was the last one handling the original case. 
October: Left another message with Tay who never called me back in September, or June.  I have left my phone number and original case number but she continues ignoring my calls.
Does anyone have any advice on this?  I'm tired of sitting in a silent house because I have no music because the customer service at Apple is terrible and just blew me off.
So far this is an issue with my Apple ID just not being able to log into iTunes on ANY computer...whether it's a Windows 7 based PC or an Apple product.  I have tried uninstalling and reinstalling iTunes on every product except the iPad (I don't use my iPhone anymore since it's old and I have a new phone). 

Answer 1

I guess Apple decided to hiccup and I was able to log in.  This was not the first time I tried this procedure, but this is how it happened.  I was not able to log in after the export from iBooks Author.  I closed iTunes Producer and then opened it through Launchpad.  I logged in with the account that is set up for the book, selected open package, and, I'll be danged if it didn't open this time.  Unbelievable...  I don't think it is what I did.  I think Apple hiccuped or cleared her throat.