Hi Martjin,
Before moving on, I'd like to confirm whether other users in your organization can access the Team site?For the steps to assign “Global administrator” role to an existing user, please refer to the link below. You also can create a new user and assign the Global administrator role.
http://onlinehelp.microsoft.com/en-us/office365-enterprises/ff637584.aspx#BKMK_2
Assign or remove administrator roles for an existing user
After that, please use the new administrator account to check whether you can access the Team site.
Thanks,
Aaron Yuan
