Yes, disconnect the computer physically from the internet and clean up the D drive by backing up and deleting files. Shut down (not just log off) when you're not using the computer, especially if you have a broadband connection.

If the D drive is too full then it can't be defragged and the computer might be trying to do automatic tasks such as defrag and be unable to complete the task.

Also, while the computer is offline be sure to shut off certain parts of the operating system that can allow other people to control your computer, such as remote assistance or any remote desktop programs it has.