If it's not a loose belt, you might suspect the front engine pulley. The pulley is a two-part gizmo -- the inner hub part, attached to the crank, and the outer pulley part. These two concentric pieces are fastened together by a rubber "donut" that's sandwiched between them and glued to both. When the glue finally fails, the pulley portion will slip -- the the rubber donut rubbing on the hub will squeal.

This pulley is sometimes called the "harmonic balancer."

A quick test is to draw a white line across the pulley, from center to edge, using a white or yellow crayon (or maybe some liquid "white out").

If the two parts are slipping past each other, the line is instantly disjointed. That is, start the engine, hear it squeal, shut it off, and examine the pulley. If the line is no longer solid, center to edge, then the pulley is slipping on its hub.

The squealing could also be bad alternator or water pump bearings. A mechanic's stethoscope should reveal this in a few seconds.
--
Don Foster (near Cape Cod, MA)