Welcome to Flyertalk!
1. Do you have an e-ticket? So can you see a 125- ticket number, if using the app? Did you make changes to the booking at some stage and they might not have ticketed correctly? If the e-ticket hasn't been issued properly, you won't be able to check-in online and need to call BA. Have you used classic.checkmytrip.com to see if there is a ticket number given there.
2. Sometimes online check-in will open later. Maybe BA are working on the flight or something. So keep trying.