I can play music but repeated nonsensical prompts to authorise and blocking syncing causing headache

Hello,

iTunes has crossed the line of nonsensical, pointless frustration now. When I plug in my iPod or iPad, I am repeatedly told that I need to authorise this computer (which is already authorised) and am presented with the wrong Apple ID (an old email address that I have not used for several years) and an empty password box. After entering both my Apple ID and password, I am told that this computer is already authorised but the process immediately starts again. I cannot sync anything I have bought recently to either device and this is extremely frustrating for both myself and my family who use the iPad for most of the time. There is no logic in how iTunes is behaving and despite uninstalling and reinstalling, I have the same issue recurring again and again. Can anyone please help me with this? Thank you.