@ ICT SLB...
Yes the Challenger is indeed built like a tank and it must have been a pretty hard upset to have damaged it beyond repair.
Well if the dual engine failure occurred at FL320 or thereafter and the RAT did not deploy automatically or was not deployed manually, I'm afraid they had lost all their hydraulics and AC electrics.
With two engines out, the EDPs on both engines for HYD 1 and HYD 2 would not be able to supply hydraulics to power the flight controls... With a dual engine failure you would have also lost all AC electrics on the aircraft which power all four electric hydraulic pumps, so again no hydraulic power to systems 1-2 and 3 which means no flight controls.
There are two backups to either a dual engine failure or a complete AC electrical failure (lost of the two main AC generators)...
- The first one would be either an automatic or manual deployment of the RAT which would then power the AC essential bus (plus some DC) thus powering the 3B hydraulic pump which would power the flight controls but as we know so far apparently the RAT did not deploy.
- The second one would be that either the APU was already running (doubtful, but not impossible, see note below) which means they had the possibility of using its AC generator to power all the AC busses and hydraulic pumps or that somehow while they were dealing with a dual engine failure and they were rolling the aircraft 5 times out of control and also descending losing 10,000 feet of altitude in the process, someone had the presence of mind to start the APU get the generator on line restoring all the AC and hydraulic pumps.
NOTE: The APU limitation on the 604 is a max altitude of 20,000 feet. Normally it should be shutdown prior to 20,000 feet, usually somewhere in the after takeoff checklist. This said it is well known that crews have forgotten to shutdown the APU and it will run (unloaded) at FL370.
Also Bombardier guarantees a successful start of the APU only up to 20,000 feet. This does not mean someone could not attempt and get a successful start of the APU at 28,000 or even 32,000 feet but I have not heard of such attempts.