itunes login

Hi. I can't get past the iCloud login window to open iTunes even though I know I'm using the correct password. I just changed it and am able to log into Apple ID at https://appleid.apple.com/ . Any help? Here is the dialog box it is stuck at:

When I type the correct password, the window goes away and then comes right back.

I need to quickly back up my phone which kinda works as it took a bath last night.

"It just works." is an embarrassment.

Thanks!!!