A loud "Screeching" sound.....Might be your starter grinding on the flywheel....If so, it could be a symptom of a couple of things (i.e. battery going dead/not charging, starter mounting bolts lose)
If you get a chance, get under the car, grab the starter and see if it moves. If so, the torque of the starter spinning my be knocking it off alignment with the flywheel....I'm no expert, but I've had it happen to me before.