Starter problems of the 2005 Chevrolet Equinox

First while driving at approx 25 mph I hit my key ring and the keys fell out. The car continue to run I just put the keys back in to the ignition when I came to a stop. I have since found that you can start the car and then remove the key and all continue to run and work. Also found that when I went to start the car the other day, once I turned the key to start it would kept running the starter. Let me explain a little better, when I turned the key to start the car and then let go the car starter continue to run until I moved the key to the off postion.

Received vehicle upon my mothers passing. Had 45k on it, garaged and only in town driving. In just over year I have had to replace rear rocker joint, ac unit, front right speaker, front brakes and starter. Now, there is a water noise under hood and truck is starting to rock when at stop light. It is also trying to run hot but no lights, leaks or issue can be found. The back spoiler was loose http before then and leaks in the back. Lift gate hard to open and moulding around front windshield is coming loose. I have 65k on this truck. There is no way this truck should have this many problems. I feel unsafe in this lightly used auto.

Several times I go to start my Equinox, and it won't start. It seems as if it over starts then shuts back off, then I have to push onto the gas for the vehicle to start most of the time but sometimes it has to sit for a minute for it to even be tried again. I have called around and has this issue looked at but no one seems to know what the issue is, Chevrolet says when it shuts off it's so that the starter doesn't burn up over time, and that's as far as it's gone.

2005 chevy Equinox awd, 3 starters, 3 coolant tanks, all coolant hoses changed, heater changed twice, a pillar panels leaked air, radiator replaced, battery bolt replaced, rear shelf broke, constant coolant smell in car, made wife sick, had car 5 months approx, spend around 90 + days in shop, dealer did all they could, but g. M. Refused to work on car under warranty anymore, g. M. " forced " to buy back under lemon law, bought Toyota, period. Have all receipts and paper work for anybody interested.

Upon starting the vehicle, it makes a rumbling and literally moves under the hood as if it won't start, but it does. It has an affect of a straight drive when starting the vehicle while it's in gear.