Q: Car going forward in reverse

I am assuming this is an automatic transmission in your Celica. There are a couple of possibilities. There is a park/Neutral Position switch on the side of the transaxle that if faulty can cause the incorrect solenoids in the transmission to activate making the transmission malfunction, in addition faulty solenoids can also cause this type of malfunction. A scan tool that can read transmission range selection and solenoid activation statuses will need to be used to determine the nature of this problem. Worst case scenario the transmission may need to be overhauled. You may want to enlist the help of a mechanic, such as one from YourMechanic, who will can diagnose your car not moving and have the equipment to read out the transmission statuses and who can recommend the right course of repair.