Starter not working

I have had this car for 3 years. 2 months ago the anti thief/immobilizer shut the car down. I tried everything. Three days later and after many attempts the car started I drove it around for about 10 minutes and parked it. As soon as I shut it off I tried to start it again but nothing happened. After 10 days of trying to start the car it finally started again and everything was great until yesterday. I did replace the battery yesterday morning drove it about 10 miles shut it off and now no start again. Any other suggestions you might have would be very appreciative. Thank you

The battery cables are fine. All the fuses are fine. Someday soon I'll be messing around inside the car and try to start it and it starts and drives great with no issues for a couple of months then it stops again. It's stupid crazy stuff. Maybe it's the alignment of the planets or swamp gas I don't know. I'm a good backyard mechanic but I've never come across a situation like this.

Thank you for the diagrams. Yes, I have checked all wiring and connections the last time the car stopped and I checked everything again yesterday. Still nothing. All the dash lights come on but that's it. I just don't understand why the car does this. There has to be a way to fix this. Do you have any more suggestions I might try out? Thank you

Yes no corrosion good connection.

Thank you for the diagrams. I checked everything possible with no luck. I hope one of these days the car will start like it did before. Like I said before I have no idea what causes this and how to prevent it from happening again. I know there can't be much more to do and I can't afford to take it to the dealer at this time. I thank you guys for all your help. I will continue to check this, that, and the other.
Stay cool my friends

No.
I've got another issue. As I was unscrewing the last screw to take the cover off the steering column this loud buzzing sound came out of the speakers and wouldn't stop. I put the key in and turned it to all positions and it only stopped when it was in the start position. I disconnected the battery and continued with the cover. I took the radio fuse out and reconnected the battery and checked all the connection. Everything checked out fine. I put the fuse back in and turned on the radio but nothing came out of the speakers.
What do you think has happened?

Thanks for the information. No corrosion. As far as the can scan goes I just can't afford to rent a scanner at this time, but as soon as I can I will. Thank you anyway guys.

Sorry I took so long to reply.
Here's what happened in a nut shell. Nothing worked. I tried everything. So I quit playing with it. 2 weeks ago I got back in to it. I turned the key to see what would happen and I heard a single click from the starter and every time after that(about 5 times). I took the starter out had it checked it was bad. Bought a new one started right up. Runs great again. Don't know how long it will last this time.
I can't thank you guys enough for all you have done for me. You guys rock.
I have one more problem though. When I take my foot off the gas the car jerks to the left not real bad but enough to notice. I had CV axles installed about 18 months ago and right after that I replaced just about everything on the front end. I don't want to sink any more money into this car. (I'll be buying a new truck in mid November). I would like to know what is going on though. Any more help from you all would be awesome. Thank you in advance. 1 more question I would like very much to donate a couple bucks to you guys as you totally deserve it. Let me know