Systems and methods for operating a driveline of a hybrid vehicle are presented. In one example, a boost phase of a procedure to close a driveline disconnect clutch may be cut short in response to an engine changing state from not rotating to rotating so that the engine may be restarted in an alternative way. The system and methods may also predict a degraded engine start from a low engine cranking speed or a long cranking time duration so that the engine may be started in an alternative way to increase a possibility of starting the engine and decrease the severity of degraded driveline disturbance.