Hope you are doing well and sorry for the trouble. As described you are unable to use the measure tool as it is not highlighted.
What is the version of the Adobe Acrobat DC you are using? To check the version of the application go to Help > About Acrobat and make sure you have the latest version 21.01.20142 installed. Go to Help > check for updates and reboot the computer once and check if that helps.
Please try to repair the installation (Windows Only). Go to Help > Repair Installation and see if that works.