Bad Starter???

[jenglin]

I have a 1988 TriStar w/ a Ford 351W and I went to start it tonight and the starter would not stop even after I turned the key off. The only way I could get it to stop was disconnect the battery. I went as far as to disconnect the key switch and put the postive back on the battery and the motor turned over. One time the motor started and the starter still kept turning. I disconnected the ignition b/c I thought it was stuck in the "start" position. Is the starter or the celinoid bad? I just replaced the starter relay earlier this year. Any feedback would be appreciated. Thanks!