I am having trouble getting my '03 Corolla to engage when I shift gears. Yesterday I backed it down my driveway a bit. Put it in park and put on the emergency brake. Today, I go to drive, start the car just fine, take off the emergency brake and try to put it into reverse and the gear won't shift. The gear shifter itself will move, and it moves very easily with no resistance, but the engine won't engage with whatever gear I'm attempting to put it in. I have checked all fluids, everything is topped off and new. I have tried putting it into gear and THEN taking the emergency brake off. Nothing works. Any suggestion of what I can do to resolve this myself? Has anyone else ever had this issue that they can direct me to the problem and what needs to happen for it to be fixed? Thanks for the help...