Starter runs conrinouusly when starter is hooked up. I have already replaced the starter relay and that was not the problem. Any advice?

The relay is not your problem; it's the starter contacts.

The starter has a magnetic switch assembly attached to it (it's the part where the positive cable is attached). Inside is a set of copper contacts and a plunger. When the contacts get worn from use, they can/do develop a ridge which can trap the plunger, keeping it engaged. Contacts and plunger are cheap and easily replaced.

DON'T hook it up until you get this fixed. If you do, you'll end up frying your starter, alternator, and possibly even starting a fire.