Are yours the bookshelf type, with the AMTs set into the face, or the floorstanding type, that look like a stubby stele, or truncated square pyramid?
The crossovers in the former are neatly mounted on a board, fairly stable and easy to remove and work on in one piece; in the latter, they are surprisingly fragile, with inductor coils wound from thin wire usually literally dangling, if they have been moved much or opened or had the woofers removed. These things are pretty easy to damage, but equally easy to repair. At least, this was my finding/experience with one example of each type. My impression may not be entirely typical, though, as the floorstanding ones I got had been so badly handled that the cabinets were literally splitting apart at the seams(!).
In either case (no pun intended), as others have suggested, these crossovers are repairable. If yours are the more common floorstanding type, check all the wires and connections, first: you may even be able to find the problem and repair it yourself.
If not, take it to a shop/tech and have it done. These are not very difficult to work on, and are definitely repairable.
Of course, if you find a good price on one from a parted-out speaker, that is also a viable option, but you don't have to go that rout.
Perhaps a good start would be to remove the crossover, and post clear pics of it here. If you are lucky, we can spot the problem just by looking at it.