Wiring Problems Engine keeps cranking without a key in ignition

I just purchased a 1994 Ford Explorer limited and it ran great and started fine. Since this was a vehicle that had been close to salt water, I looked under the hood and realized alot of things were corroded. I came out the next day to clean it and the battery was dead and with a new battery it wouldn't start. It acted like it was going to but didn't. I then replaced the battery cable ends and cut off the corroded areas. I hooked the new ones up and then put them on the battery posts. There was no key in the ignition, but the starter started cranking over!! I immediately took the battery cables off. I then replaced the starter with a new one and looked for any worn or loose wires and found nothing. I then unhooked the negative cable from the engine block since it appeared corroded. With the negative cable unhooked and not touching anything, the engine cranked over continuously when the battery cables were hooked back up!! I am about to scream. Can ANYONE give me a clue? I appreciate any and all help! Thanks, Tom

You hooked the wire to the wrong terminal of the starter solenoid on the fender. There should only be one wire on the terminal that goes to the starter. So, basically switch the new battery wire to the other terminal. Now don't you wish that you had used masking tape to mark the terminals! You're not the first one. Have seen this same problem a couple of times.

When I replaced the cable ends, I did one at a time and just cut a little extra off each wire to do away with the corroded part. I did the positive cable end first, finished it and then the negative cable end. It was exactly as I received it when it ran great, so me having crossed a wire couldn't have happened. It COULD have been that way when I got it. Is it Possible for the solenoid on the fender to have broken and to remain open causing my problem? Thank you for your help. I appreciate it, Tom

I'm not going to play the blame game. You will find that the wiring is different from the following.

On one of the large terminals there should be 1. wire from the battery 2. wire to the alternator output 3. wire to the distribution fuse box.

The wire on the other lug only goes to the 1/4 inch tab on the starter. The possiblity of this relay/solenoid shorting is almost zero. You can remove this wire and the starter should not turn if you have to do further diagnostics.