I went out to start my 89 F-150 the other day and it wouldn't turn over. I heard the initial hum of the fuel pump and then there was just a humming or buzzing sound. It made this same sound when I tried to blow the horn. Today when I turned the switch on the fuel pump kept running. It did not stop after a few seconds after it usually does. It did not stop until I cut the switch off. Could this be a starter problem or something else? It has a new solenoid switch on it.

If that has the solenoid up top, and when you turn key and you have good power to Starter, it would be at the Starter or ground.