2002 Honda civic, car still moves when put in park

http://sheehan.com.ph/batteries.html

https://www.vehiclehistory.com/articles/2002-honda-civic-battery-avoiding-a-mistake

https://everythingwhat.com/what-is-the-meaning-of-sm-in-battery

car is cold and moving is OK if not moving getting hot could be thermostat stuck close or rad.is clog.

Never have a trans flushed. Unless it was at a dealer, the wrong fluid was most likely put in, Unless you saw them put HONDA ATF-Z1 fluid in. Check the fluid with the engine off.

make sure the shifter is totally in park.try pushing the shifter past or as far as it will go into park and try turnning off and pulling the key out

the cv shaft is not installed correctly and is not ingauging the splines,its grinding because the transmission is going around and your trying to put it in park

Would need more info on the heat/ac problem. But on the shifting problem check under the hood and make sure when the shifter is moved the linkage moves. If not the shift cable is most likely the problem, but check at the shifter to make sure.

Check the wires with the car in reverse and the key turned on, use a meter. On cars the black is usually the ground but you need to check to be sure.

Its the parking pal in the transmission that's bad but let me ask something was the car in drive when this happen? if so then it's normal but if it was in park then it's not normal. The parking pal in the transmission is bad. Have a nice day

When you say it's running like a truck check this out for me, start your car let it idle in park for five minutes then keep your foot on the brakes shift your car into drive check how it runs does it run better in drive or when you put it in park. If its better in park your problem is in the transmission. Have a nice day buddy.

This is an almost un heard of problem. But it seems to me there is an electrical issue with your transmission. I'll explain why... If this was an actual mechanical component you could not turn off the car, then put back in drive and it work normally. So its definitely an electrical item that is reseting when you turn the car off, and then working again for the same amount of time it did the first time. Now the good thing is if you will take your car to a honda dealership they will fix this problem within an hour. Just make sure you go to a certified Honda dealership. Shouldnt cost ya that much most cost will be for the electrical part you need. Labor will run about 35 dollars an hour.. But like i said 1 hour should do it. So take 100 dollars for labor and the electrical component shouldnt be too bad i think you will be just fine man