We know that Professor Hardacre is killed by one of the Ager brothers after trying to take the crown from Saxton, but we don't know which one of them does it. There are reasons why it's likely that William Ager is the killer.
First, in the painting of the four Agers, Thomas and Frederick's images are burned after being thwarted by Nigel, leaving two figures, one of whom is holding the sickle used to bludgeon Hardacre. There's a fifty-fifty percent chance that the man holding the sickle is William. The man holding the sickle appears to be the youngest of the four, and William died of Tuberculosis at the age of thirty-one.
Also, the ghost of Verity church warns that a dangerous ghost called William is going to 'chop off his head' if Nigel doesn't leave the crown alone, implying that he is in possession of a bladed weapon of some sort. All these points suggest that William is the man holding the sickle in the painting, and he used that sickle to kill Hardacre.
His name is never stated, so he could be Oliver's kid brother. The real Oliver might be home sick, or he could be sitting this year's contest out so his little bro can have a shot at winning.
- Probably confirmed in the demo version of Blackenrock, in which Oliver appears much more prominently and looks at least two or three years older than the kid from Lost Crown.
The date of Nigel's recruitment and on the package Hadden sends for him are from 1978, yet Nigel is clearly from a more recent time (clothes, hairstyle, references to the Middle East and TV celebrity chefs, etc). Hadden's note from the package suggests it was written after their phone conversation, even though he refers to the package having already been sent that morning during that discussion. Much of this can be reconciled if Mr. Hadden is actually observing Nigel by mystical means from 1978, and leaving directives to Hare and Crow that they can carry out in 2008.
The documents Nigel stole depict a supernatural Swirly Energy Thingy very similar to the one in Ganwulf's tomb. Letting Nigel get interested in the Lost Crown, and recruiting to investigate the ghosts that could lead him to it, was just a sneaky way to gain access to one of those.
Nigel hears a distressed cat's ghostly meowing from inside the chest in Harbour Cottage, yet the person arrested for the catnappings ( Mr. Gruel) didn't have a key to that place. Morgan did have one, so could have used the Cottage to hide the kidnapped cats until they were weak enough to handle easily and she could sneak them into the old Net Hut. One of the cats was left in the chest too long, and suffocated, creating a meowing ghost, exactly like the one that he later hears behind the door to the Nightmare Room.
After Nigel occupied Harbour Cottage, she couldn't use it anymore, which is why Mr. Tibbs was strong enough to escape her at the Hut. Then she framed Gruel to deflect the investigation when Nigel and Lucy uncovered evidence of her crimes.
Normally, they wouldn't bother to start plaguing a would-be Crown-hunter until the trespasser got dangerously close to its hiding place, which is presumably why they hadn't killed Hardacre years ago. However, the Hadden photos of the Chasm had enough of a supernatural aura of their own to worry the Agers: they know the other ghosts in the region have information about the Crown's location, and the photos' presence implied that this treasure-hunter might try to communicate with those ghosts, so the Agers tried to head off Nigel's investigation by scaring him off in Hardacre's guise.