when you removed every piece of the engine off to get access to the timing belt, did you move the power steering reservoir? if so, this can cause the fluid to be uneven and have air in the power steering system, causing the power steering pump to make whiny noises and malfunction.
Solution:
1. make sure the car is in the OFF position.
2. jack up the front of the car making sure both the front wheels up not touching the ground.
3. as added caution, put jackstands under each side.
4. put your Toyota Celica key in the ignition.
5. turn the key to start the engine.
6. get out of the car and remove the cap from the power steering reservoir.
7. get back in the car.
8. turn the steering wheel clockwise slowly all the way. when it reaches the end, do not go any further.
9. turn the steering wheel counter-clockwise slowly all the way. when it reaches the end, do not go any further.
10. repeat steps 8 and 9.
11. repeat step 10.
12. repeat steps 8 and 9.
13. repeat step 11.
14. keep turning the steering wheel until noise from the power steering pump dramatically changes.
15. get out of car.
16. wipe off power steering fluid excess which have overflowed due to bleeding the air out of the power steering system.
17. refill the power steering fluid and top off to the MAX or FULL level.
18. recap the reservoir.
19. turn off engine.
20. jack the engine 2 inches higher.
21. remove jack stands.
22. lower the vehicle using the jack.
23. restart the engine and test drive.
24. inspect for noise and steering response.
note: if the response of the steering has not completely returned, repeat steps 1 through 24. Repeat the steps as many times as needed to bleed out the air in the power steering system.
Cliffs: air in power steering system, bleed it out.