Webby, its the starter relay and its connector. Its essentially an electronic switch that tells the starter motor to do its job. This ones f*&%$, so it cant send current to the starter motor to crank the engine.
Its located on the lower left, between the battery and the starter motor. They are prone to picking up moisture and dirt, resulting in what you see in the pics................Pays to check em from time to time.................
Laurie