Sorry to hear about your troubles.

First the obvious: are you sure it’s the website that isn’t working? Could it be whatever device/browser you are on? Many airlines have apps now, can you book a ticket on the app?

Most airlines still have telephone numbers, you can try calling them, although they will probably charge a fee to book o er the phone. If the airport is close to you, you can also still go to the counter and buy a ticket if you need to. (Again, they will charge a fee for that.) However, if you explain the situation to an actual human they might have the latitude to waive some of the fees.

However, you might also want to check to see if a different airline can get you there with a connection. flights.google.com is a very good search engine for that now. Just put in the two airports, and it will show you all the flights you can take.