OK, going back through to get all the info on the Predator's crystals as I can before I have to return the book

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Per Chapter 2, the main lift crystal sustained a crack from providing the power for stopping two dives in a very short amount of time. 

Per Chapter 7, three of the trim crystals also needed replacement-- probably as a result of the strain of making up the difference in lift from the damaged lift crystal.

Per Chapter 28, Albion provided Grimm with eight(!) new(!) trim crystals for the Predator as well as a brand new lift crystal spec'd for a battlecruiser ("Mark IV-D").  The new crystals are apparently more efficient/powerful than the old.  The core crystal (apparently undamaged) is mentioned as 'exceptional'.

In Chapter 40, Master Ferus says that he's going to have a word with the Predator (and remarks that she is 'insouciant' but cooperative).  The power core is not mentioned as being either online or offline.

In Chapter 49, Gwen hears the hum of an active power core crystal (probably the same thing as a power core and aforementioned core crystal).   The power core is apparently a first generation (1kyr old +) one and is therefore very efficient in comparison to most others--which in combination with the very powerful new lift crystal could provide enough lift to (fatally) damage the ship.

In Chapter 61, the power core flares as the shroud absorbs a hit from etheric cannon.

In Chapter 63, Folly senses some sort of intelligence as they lift off.  This intelligence scares her-- and its speech implies that it might at once point consider her a threat/something to fight. This voice-- confirmed to be that of the Predator herself-- also says that Grimm can hear her better than all but etherealists.

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So, you're correct: the Predator crew received/replaced all of her auxiliary crystals-- lift and trim, but *not* her main power core.  I am slightly confused by the difference between Master Ferus' reaction to the ship and Folly's: I don't think the ship was powered up when he spoke to her.  And while she didn't seem to speak with the Predator on the way down to Habble Landing, she definitely noticed (and was noticed by) the Predator as the Predator began to chase after the Mistshark.  I take this as confirmation that she hadn't spoken with the Predator previously-- she wouldn't have been as surprised. This may be as simple as the ship communicating with Ferus on the way down/not noticing Folly because of Ferus, or it may mean that the power core has to have a certain amount of load on it to 'wake up'.