I checked battery voltage is with in specs, shifter moves up and down like usual with a few rpm bump every time. I also checked the axels by lifting the tire left and right and they don't turn wich tells me they are not broken. The only thing I found is the driver's side axel boot close to the tire is torn and leaking grease all over. When I first checked the coolant level was low and it was spilled all over the engine compartment.
My car has 150000 miles.
My car has an automatic transmission.
You need to check the transmission fluid level to see if it is low. This would cause the no transmission engagement. If fluid is full then you have a transmission shift control valve issue which will need to be tested for pressure loss or there may be a front transmission pump that has failed.
These checks should be done by a transmission mechanic with the proper test equipment. However, feel free to contact a qualified professional who can come to you and diagnose the issue with your gears if you’d like a second opinion on this. Good luck.