Cannot Sign in to Messages or FT on Mac Air

Both messages and FT stopped working on my husband's Mac Air (purchased end of 2016). They worked for about a year and then stopped working in January, 2018. At the time, my husband didn't really care, but now we'd like it to work. Both apps are signed out and we receive error messages when attempting to activate. Sometimes "an error occurred..." and sometimes "the user name or password is incorrect." I have tried several things. I confirmed the Apple ID and password on the Manage your Apple ID site. That was successful. Family sharing works between our devices. I closed and reopened the apps, rebooted the laptop, and attempted to sign into Messages with his Apple ID on an iPad and that also did not work. He is signed into iCloud on his Mac, but when I got a message that there was something wrong with his iCloud and got a box to sign in, that was also unsuccessful. I am afraid to sign him out of iCloud, lest we be unable to sign back in!! Thank you for any suggestions, especially the one that works!!