Well, it could be any number of things. If the wires connecting the panel to the crossover have just come loose, you should be able to reconnect them easily. The cover on the electronics box is easy to remove.
If the wires to the panel have broken off, it might be a little more costly, because if they broke off close to the panel, you'll need to replace the panel. You can order replacement panels from ML for a few hundred dollars, and they are easy to swap out. The repair shop that quoted you $2000 to repair one SL3, ESPECIALLY since the electronics are still OK, is a ripoff. I would never go back to them again...
I own original Sequels, and the top of the crossover box is held in place by just a few screws. I think the SL3 is similar, and once you get the top off, all the connections should be easy to see and work on. Maybe a member here with a LOT more experience with the SL3 can help you better though.
You should send a private message to JonFo. He's probably got more experience with hacking the Sequel line than anyone on this forum. He can probably get you up an running in no time at all...
Oh, yeah, one more thing--Welcome to the forum! We'll do our best to help you get your SL3's back to sounding their best, and we're glad to have you here, even if it is under such unfortunate circumstances.
On the other hand, maybe it's time to sell off those kids, and buy a new pair of Summits...
--Richard