I have tried logging in with my production org credentials (as sysadmin) and on my dev org (as sysadmin).
I have the right to download AppExchange packets on both accounts.
I have cleared all cookies and retried.
In the Login History on the accounts I can see that the appexchange_api successfully logged in with Remote Access 2.0
 

What happens is:
I press ”Get it Now” and a new window pops up “Login to AppExchange"
I click “Open Login Screen”
Yet another window pops up: “appexchange_api is asking to: Access your basic information”
I click “Allow” on the prompt in the new window and after a while I get the response “Login Successful” after which nothing happens
Both windows are open and nothing happens

Thoughts anyone?