One would normally expect this problem to begin with a bad starter (lack of lubrication of the Bendix drive or worn parts in the Bendix or both), but it soon grows into a ring gear problem. When the starter is removed, look at the ring gear through the starter opening while someone else turns the engine over slowly by hand. An engine will usually stop at the same spot, so each time the starter fails to engage and causes the screech, it chews a little more away from the same spot on the ring gear. The engine will also have a second favourite spot 180 degrees away from the main one which also may have some wear. A new ring gear will cost close to $100 from Volvo and is not hard to install at home (once the transmission and flywheel are out).