I suspect it was a "Bleeds Off" takeoff, which may have helped the situation immeasurably.
Deicing was being done in LGA, and even if you don't deice yourself, a bleeds off takeoff (APU running, supplying air for packs) will stop a lot of the stink of sucking up Deicing fluid on the runway, AND that crap is slick and a lot ends up on the runway, so I tend to always go bleeds off/MAXpower when deicing is being done (regardless of whether or not I deiced)especially at LGA with the short unforgiving runways.
If the APU was running for takeoff then there was no rat deployment at all, full electrics were always available, and a simple push of the yellow electric pump would restore much of the hydraulics if the engines weren't even windmilling.... On the otherhand, to restore the blue system the RAT manual deploy button would have to be pushed with the APU running...
IF the APU wasn't running, then the crew was even busier (though they may have immediately pushed the start switch at the beginning of the event) will be interesting to see.
Good job all around, can't wait to read the cvr transcripts and the reports...
Cheers
Wino