Unsure if this will help anyone but I had the same problem with the message always coming up when I tried to login: "We could not complete your iTunes Store request. The iTunes Store is temporarily unavailable. Please try again later."
What I couldn't understand was that I could log into iTunes online, but not through the iTunes app, becoming very frustrated I went to drastic measures to get everything working again - although I found this post after I had success.
To add to the issue, my iPhone (4S - iOS7) was visible on iTunes (latest version), but some of my apps had failed to sync (showing grey on my iPhone and being unable to delete them), causing further issues and adding to my frustrations....which attributed to the drastic measures posted below.
(You may want to try following the above posts before following my method)
--------------------------------------------------
**** Apple support provided me with an email containing many links, all of which didn't really help me, but I'll post anyway, just incase they assist someone else:
"Dear Luke,
Thank you for writing to iTunes Store Customer Support, my name is Indra and I'll be assisting to you with your concern.
I understand that you are unable to login to your iTunes store account and getting message that the iTunes Store is temporarily unavailable. I can imagine you must be eager to access your account and I will do my best to resolve this issue.
Luke, as an advisor for the iTunes Store, I handle issues related to billing, downloading, customer accounts, and the items available on the iTunes Store. Although your question falls outside of my area of specialty, I will be happy to assist you with resolving your issue.
I have verified that the iTunes Store is functioning and accepting connections. The issue could have been temporary, related to your internet connection, your local network, or your computer itself. If you’re still unable to connect, this article outlines some potential solutions:
Can't connect to the iTunes Store
http://support.apple.com/kb/TS1368
These articles have helped other Windows users resolve connection issues:
iTunes for Windows: iTunes Store connection troubleshooting
http://support.apple.com/kb/HT1527
iTunes for Windows: Could not establish a secure connection to the iTunes Store
http://support.apple.com/kb/TS1470
iTunes for Windows: can't access the Internet if proxy settings are incorrect
http://support.apple.com/kb/TS1490
iTunes: Troubleshooting security software issues
http://support.apple.com/kb/TS3125
Firewall, virus-protection, and web-acceleration software can prevent you from connecting to the iTunes Store. You might not be able to connect even if the software appears to be configured to allow full access to the iTunes Store. You can use the MSCONFIG utility to determine if software on your computer is preventing access to the iTunes Store. For detailed instructions, please refer to the following article:
Using Msconfig to troubleshoot conflicts in Windows Vista and Windows 7
http://support.apple.com/kb/HT2292
If the articles above don't help you connect to the iTunes Store, I suggest testing to see if this issue occurs while you are signed in to a new user account on your computer. To learn how to create a new user account in your version of Windows, please read the article below for your operating system:
How to create and configure user accounts in Windows XP
http://support.microsoft.com/kb/279783
Windows Vista: Create a user account
http://windows.microsoft.com/en-US/windows-vista/Create-a-user-account
Windows 7: Create a user account
http://windows.microsoft.com/en-us/Windows7/Create-a-user-account
Windows 8: Create a user account
http://windows.microsoft.com/en-us/windows-8/create-user-account
Once you are signed in to this new user account, open iTunes and try to connect to the iTunes Store. If you can connect without error, then you’ve identified that the issue is with the previous user account that you were using. You may want to consider adopting this new account as your user account and transferring your files from the old account to your new one.
If you require more assistance, you may wish to call our AppleCare technical support team. A technical Advisor will be able to tell you about Apple's complimentary and fee-based support options as well as assist you in determining what option might be most helpful in this case. To find the appropriate phone number, please visit:
Contacting Apple for support and service
http://support.apple.com/kb/HE57
I hope that the information provided above is helpful.
Thank you for contacting us and have a nice day!
Sincerely,
iTunes Store Customer Support
http://www.apple.com/support/itunes/ww/"
--------------------------------------------------
But if the above doesn't work for you then you can follow my method...in the end, I perfomed the following actions which did work:
1). Uninstalled iTunes from my computer (via Control Panel > Programs & Features)
2). Located the iTunes folder containing media, Previous Libraries etc (normally located under your Music folder) and simply moved it to my desktop. (can't afford to delete)
3). Downloaded iTunes.
4). Plugged my iPhone into my laptop and moved all contents across to my desktop (photo's).
5). Restored my iPhone erasing ALL data (extreme but desperate measures were required) - you may want to back it up, but I personally didn't have anything that I couldn't afford to loose on it.
6). Set-up my iPhone (set language etc...) including iCloud, but did not plug it into my laptop.
7). Chose the following iPhone settings>
> iCloud - Contacts turned off
> Mail, Contacts, Calendars - iCloud Contacts turned off (same end result)
> iTunes & App Store - made sure I was logged in via Apple ID.
7). Closed Outlook.
8). Re-installed iTunes, saving it on the C:> default location.
9). Followed the normal iTunes install prompts, setting it up as new. (making sure I had NO apps or music - clean slate)
10). Plugged my iPhone into my laptop, waiting for it to appear as it normally does.
11). Checked for iOS updates and iTunes updates (all good)
12). Checked Sync Contacts with Outlook (opening Outlook at the same time) - Calendars I left to the iCloud
13). APPLY....once sync finally completed (this time SUCCESSFUL) I was able to click iTunes Store and LOG IN.....finally!
-------------------------------------------------------------------------------- ---------------------------------------
I probably didn't have to perform all 13 steps, but that's exactly what I did to get everything working again!
There is probably someone out there who will be able to explain why I couldn't login to iTunes, why many of my apps didn't load onto my iPhone correctly, why everything failed to sync and probably able to shorten the above 13 steps to a quick fix.... but for now, everything is finally working and my 48hrs of frustration has come to an stress free end!