I had the same problem with the 64-bit version of iTunes with Windows 10. I tried all the different browser and it still didn't work. I kept getting the window to install iTunes, even though I already have the current version. Finally figured out another way, so I thought a would share:
Go to the Disney Movies Anywhere app (I used an ipod touch)
Go to "More" at the bottom right corner to access the setting menu.
Go to "Connect Accounts"
Select "iTunes"
I was prompted to confirm and enter my apple password.
The accounts are now connected again. My accounts were linked before but apparently the connect expires and has to be reconnected.