vehicle doen`st engage gear when engine is running
You correctly diagnosed a broken transmission.
So why did you post?
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Have the car towed to a mechanic and/or transmission repair shop.
This is not hard.
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I’m guessing you have an automatic transaxle (transmission), also guessing that when you move the gear shift lever from P (park) to R (reverse) and or D (drive) that nothing happens…
1st Question, does the shifter feel easier to move, much less resistance??? if so then you may have broke the shift cable or even the end bushing broke off the shifter or transmission…
2nd Question, does the vehicle make any kind of noise or clanking when you shift into R or D??? Possible Axle broken
3rd Question, is the ATF fluid full (vehicle has to be running at normal operating temp and on flat ground to get accurate level, also what color is the fluid and does it have an offensive odor/smell burnt???
4th Question, had the trans been acting up or showing/given any warnings something was wrong?? Had any work been done on the vehicle recently???
Toyota transmissions are not normally know for going bad under normal circumstances, but anything can break at any given time with out warning… Sometimes when a trans just out of nowhere just stops working it means the torque converter went bad or the front pump stopped pumping for what ever reason… An automatic transmission/transaxle is one of if not the most complicated component on a vehicle… Your Corolla should have an A245E trans in it and the know problems with them are:
Toyota A246E fits 2003 to 2008 model year Toyota Matrix with the 1.8L 130 horsepower engine, 2003 to 2008 A245E with EPC solenoid in Toyota Corolla with 1.8L engine as well as 2003 to 2008 A246E two-wheel drive Pontiac Vibe.
Common complaints with these transmissions are shuttle shifts, bind-up or flare on the 2-3 shift, slips with throttle in 3rd or 4th, kills engine at a stop as well as TCC slip codes.
The first area of concern leading to the TCC complaints is a worn-out TCC relay boost valve and bushing. When the TCC relay boost valve and bushing wear out, lock-up control and overheating complaints occurs.
The other area of concern is a worn-out solenoid modulator valve bore. The purpose of solenoid modulator valve is to limit the pressure going to solenoids, just like an AFL valve or solenoid pressure regulator valve does on other units. The modulating valve and spring are calibrated to prevent solenoid feed pressure from exceeding a predetermined PSI, no matter what main line pressure is. This is necessary to prevent more fluid from being fed to the solenoids than they can effectively regulate and to limit what max line pressure output is. If the pressure feeding the solenoids is too high or too low, output will also be too high or too low. Consequently, shift quality complaints, solenoid performance and gear ratio codes can occur along with low or high main line pressure.
Here is what the A245E looks like in exploded view, not counting the valve body or torque converter…
https://www.wittrans.com/img/diagrams/65/65.jpg
As stated by Mustangman and Ledhed75 in the other post, you probably need to have the vehicle towed to a qualified transmission shop…
OP, suggest to clarify your Corolla’s transmission configuration, automatic or manual?