After killing (killing...?) the ghost, read the note and go to the lower left-hand cornere cell. There's a blanket there. Click on it to reveal a tunnel leading down. Note: reading Edmund's note is optional. The ghost is just there for the much needed experience points.
Well, you didn't finish that one really, although the answer for the Edmund quest is pretty far-fetched.
Once you're in the cell, you have to click on the cracked wall to break it down, so you can go down and talk to Edmund. Make sure you tell him he's dead.
Now all you have to do is prove that he's dead. Walk back up, and go to the cell on the right side of Edmunds's cell. Walk around a bit in that cell, until your deathknight comments on how much he hates rats. Kill the rats, pick up the bone they drop, and go back to Edmund. Now all you have to do is show Edmund the bone, and he'll die conciously.
NOTE: If you convince Edmund he's dead, you can't talk to him anymore. Make sure you learn everything he has to teach about magic. You'll need 60 gold to do so. You should be able to find that amount before reaching Fergus even.