Problem: One Drive for Business options are grayed out and the menu with new, upload, etc. does not appear.
This issue is caused when you have an account manually created in Office 365, then the account is deleted, then you federate your Active Directory with Office 365 and the account is recreated. SharePoint has a unique Passport User ID (PUID) that was not removed when the account was deleted. When the account was federated and recreated, it also created a mismatch on the PUID causing the issue.
Solution: Unfortunately, this is not something you have access to fix yourself. You must contact Microsoft Office 365 support and report the issue so they can fix it on the back end.
Users report the issue here: Office365 User Troubleshooting
Administrators report the issue here: Office 365 Service Request. If you have multiple impacted users, you can submit them under one service request.