MacBook Air keeps asking for my Apple ID
I keep getting recurring requests for iCloud password. When I enter my Apple password it asks me for a verification number but doesn't open a dialog box to allow me to enter one. I have to go back into my account preferences on the website and enter the verification number sent to my iphone that way. I have now turned off the two-factor authentication, but I am still being asked repeatedly for my iCloud password on my Macbook, and also being told my iPhoto cannot connect to iCloud.
Any advice? Thanks
MacBook Air (13-inch Mid 2012), OS X Mavericks (10.9.5)