Starting off
Speak to Brother Kojo and he will ask you for the time. You are unaware of the time just as everyone else since the clock tower is broken. He will offer to pay you if you help repair the clock. He will explain to you the issues: there are four cogs down in the cellar which are too heavy for him to carry. He needs you to pick them up, one at a time, and take them to their location.
Climb down the ladder and then head out to the main room with the four colored tiles. Each tile has a door which corresponds with it. The door which corresponds with it is the closest door. These are an important key to finding the cogs.
Black Cog
Head through the door which corresponds with the black tile. Head all the way through the coridor until you reach the fire with the spiders surrounding it. The cog is located in the fire. Now is the time to use either your ice gloves or the bucket of water you have.
Take the cog and head to the ladder. You will see an area with clock spindles. Use the black cog with the black spindle on this floor.
Blue Cog
Head through the door which corresponds with the blue tile. Once you reach the end you will find the cog locked in a room. You will need to find a different way in.
By the zoo there is a ladder. Climb down the ladder and walk all the way through the corridor until you find the wall that you can push. Push the wall, pick up the blue cog, and then climb up the ladder. Head to the room with the ladder and then climb up the stairs. Use the cog on the blue spindle on that floor.
Red Cog
Walk through the door which corresponds with the red tile and run through the level-53 Ogres and pick up the cog. Take the cog and use it on the red spindle on the main floor. (floor Brother Kojo is on)
White Cog
Walk through the door which corresponds with the white tile. Grab the rat poison at the end of the corridor and then go the other direction until you reach the two red levers. Pull both levers and then use the rat poison on the food trough in the rat area. The rats will die and rumble the door hinges loose. Grab the white cog and head to the top of the tower. Use the white cog on the white spindle.
Wrapping it up
Speak to Brother Kojo and tell him the clock is now fixed. He will congratulate you and...
