Like most aircraft, the F-16 stores some of its fuel in the wings. Plus it was prepped and ready for a flight, which means its tanks would be full. So, when the wings were torn off, the resulting fuel leak would have burned the jet up immediately.
When Jack releases a rocket while sitting in the (fake) F-16, it clearly falls right in front of the left wheel, which should make moving forward impossible. Without anyone removing the fallen rocket the plane could not have moved forward.