Using New Outlook on Windows for personal email, calendar, and contact management
Hi! Sorry to hear that you are having trouble with this situation. Unfortunately, if the account is blocked because the mailbox or Microsoft cloud storage is full, the only way to restore sending and receiving is to free up enough storage or add more storage to the account.
If you have already moved some files to your PC, please make sure those files are no longer stored in OneDrive or Outlook.com, and also empty the Deleted Items/Junk Email folders and the OneDrive Recycle Bin if applicable. Moving files to your computer will not reduce the online storage usage if the same files are still stored or synced in OneDrive.
After freeing space, it can take some time for the available storage to update correctly. If it was not enough, you will need to delete or move more data, or purchase additional storage. You can also use an external drive, such as an SSD, to keep a local backup of files before removing them from OneDrive.