Another common Firebird problem is the ignition switch down on the lower column. It is held on by two screws. If the screws come loose it will make the switch so that the rod that extends from the key switch not long enough to engage the starter. There is some adjustment on this switch too.
A starter itself can cause exactly what was described here. As a starter fries it takes more and more power until it will not even roll over with a fully charged battery.
