Car will not start

My car broke down on a dirt road up in the mountains, it wouldn't start again even after resting for a while. My gas was 3/4 full, battery is new the car would crank but not start. When I turned the key all the dash lights came on like they should as well did all the gauges. There was no check engine light showing and no code displayed on the computer so I tried starting again. It turned over but would not start and when I let go of the key there was a fast clicking noise under the dash and all the gauges were going crazy so I turned the key off locked my car up and started my 10 mile walk home. The next day I got a ride back to my car it was still doing the same things. I'm a 56 year old gal that's partially disabled there's no way I could push the car by myself so I did the worst thing possible, I used the starter to crank the motor and turned my car around. Stupid yes it was and yes it fried my starter. The car was towed to a friends barn where it sat for a year while I tried to get help for it. I bought a new starter and had it installed and put the car back together. Checked all fluids, put another new battery in, turned the key all lights and gauges worked fine but starter wasn't engaging. I tried again a few days later this time all there was is a weird sound coming from the starter that sounded like electrical possibly? I don't know what to do, i'm scared that I have hurt my car and can't afford the repairs it needs now.

I had someone give me a push the other day and my car started right away when I let the clutch out, no sputtering, wasn't sluggish in fact it did great for a car that had been sitting over a year. Now i'm really worried this will be an expensive repair, God I hope not. Thank you in advance for taking time to read my message and for any help or advice you can give me.