Ignition problems

Hi there. I have a 1998 Dodge Stratus that was working fine up till today. I started the car a few times today due to the cold weather and on the last time, the car wouldn't start. Just click, click, click. What is weird is that the lights, oil light and electronic odometer never went out with the keys out. I towed it to a shop where they boosted the car. Car started except the starter does not disengage. Also, when you turn the key, the car starts at the accesory stage. I have replaced the battery and also have noticed a fuse under the hood that was blown( can't remember which one, but it was a 20). When I replace that fuse, the car starts automatically without a key. I was told by a friend that it could it be the ignition switch that may be stuck? Any ideas?

The starter or wiring at the starter coil is shorted and needs replacing.
RG

starter solenoid may be bad

Could be the ignition switch, lights should turn off when key is out and shouldn't start without key in.

Your friends sounds pretty good advice, check into it.