If the vehicle will not crank over, the most common problem is the starter, which tend to fail at about 100,00-125,000 miles. Sometimes it is only the starter solenoid contacts, but often the complete starter (including solenoid) needs to be replaced.
Engine Won't Crank Due To Starter on Toyota Celica
Average mileage: 111,666 (100,000–125,000)
12 people reported this problem
1994 Toyota Celica 110,000 mi, Visitor
Car won't turn over when I try to start it only makes a single click nose
1990 Toyota Celica 125,000 mi, Visitor
In shop now, unsure if it just the celanoid or the whole starter