If the defendant doesn't want any kind of settlement, the case will go to Tribunal.
This can indeed be several years after the purported crime happened.
Most of the time, the magi attending the Tribunal meeting will not like to have their time wasted, so very often any punishment decided by the tribunal will be harsher than whatever the proposed settlement would have been.
A Quaesitor is primarily an investigator and legal expert - not a judge.
Other than being able to call a Wizard's March in an emergency, they have no power to force any punishement on the defendant. Only the Tribunal can do so.