I installed a new positive battery cable and when I tried to hook it up to battery the engine started to crank over without key. Why would it do that

Do not ask me why this is happening but the starter is staying in gauged. First try removing battery cable from solinold again then reinstall if that does not work tap on starter solinold and starter with a hammer this should disengage starter. If it continues to do it may need a new solinold.

Wires are probably touching at the starter solenoid and I am assuming (I know, not very smart) that the starter solenoid is at the starter.

Sounds like you are bypassing the starter relay (somehow) which is bolted to the fenderwell close to the battery. Check the connections at that point. If the relay is stuck closed for some reason as soon as power is supplied the vehicle will start and the starter will remain engaged.

http://troubleshootmyvehicle.com/ford/4.0L/how-to-test-the-starter-motor- 1

Starter solenoid is mounted on the starter. After looking at some photos, I am wondering if you put the battery to starter cable on the wrong connector. One large connection is switched by the solenoid and the other large connection is hot to the starter. Hooking them up wrong will cause the starter to spin as soon as the battery cables are connected.