Talk to the crying mayor, and he will tell you that the town is deteriorating because all of their carrots have disappeared.
Visit Charlie's Carrot Surplus where the clerk tells you her cat is missing, and may be by the farmhouse.
Head left to Carrot Farm.
Go to the old house and enter it by the chimney.
Go right and take the bowl that you find next to the couch.
Go back to town and visit the Carrot King Diner. Take the bowl to the waitress and ask her to fill it up with milk.
Go back to the farmhouse and put the bowl down where you found it.
Go to the right and climb the electric wire to get upstairs. Go left until you reach the bathroom. Turn on the shower by twisting the handles. The cat will jump out.
Chase the cat back downstairs (this may take awhile, and the easiest way is to just auto-chase by clicking on the cat). The cat will drink the milk and follow you.
Go back to town and give the clerk her cat. She will give you a crowbar.
Go to the Carrot Factory.
At the factory:
Get the blueprints from the boarded window.
Climb down near the icky water to the right of the building and use the crowbar to get inside.
Walk to the left until you find the Carrot Transporter.
Entering the factory:
Climb up and go right. The last two moving floor sections may take a while to get past. (Try to stop between them.)
Continue climbing up. Dodge the rat, and go up to the main factory room.
To turn on the power, move the middle switch all the way down and the other two switches to the middle. Once it is turned on, jump up and hop on the moving claw near the top. This will take you right to the vent system.
First, head for the PROCESSING ROOM (on the lower left). Use the blueprints you found earlier to find your way around the vent system.
On your way to the PROCESSING ROOM, you will pick up a pair of wire cutters.
If you enter the room, the robot guard will transport you out of there, to :
The FREEZER room . In the FREEZER, you will find a security box. Cut the wires and leave.
Go to the PRINTER ROOM. You can disable the rabbot ears controlling the worker there (who is being mind-controlled). You do this by pressing the ears' blue control button (C) when her back is turned. She will show you a piece of paper that prints out. (It reads, "System Password: fuzzybunny".)
Go to the PROCESSING ROOM. With the security system disabled, the flying rabbot guard will not appear.
Release the workers from their mind control. You will see that the evil Dr. Hare's plant is stealing all the island's carrots to process into Rocket Fuel chemicals. Go to the big metal doors on the right that says EXIT. Because you don't have rabbot control ears, it drops you through the trap door instead. It will take you to a room with giant smashing machines.
Make your way down the belt without getting squirted or smashed flat. At the far side, you will find a pair of rabbot ears. Climb out.
How to defeat Dr. Hare:
Make sure you are wearing your rabbot ears when you go to EXIT door.
The door will open and Dr. Hare will be waiting for you. He assumes you are under his control and orders you to launch the GIANT SPACE RABBOT.
Climb up Dr. Hare's rabbot and go to the right side by the computer. Deactivate the person's rabbot ears so he will let you use the computer. Type in the password from before (fuzzybunny) and the task (launch rabbot).
A little screen will pop up, kind of like a video game. Use the joystick to steer the GIANT SPACE RABBOT into the meteors to crash it.
When you defeat Dr. Hare and his rabbot, follow the released slave up the rope to the left, and go back to Main Street. All of the citizens are grateful.
Talk to the mayor and he'll give you the 24 Carrot Island medallion.
Before you leave, check the farmhouse. The carrots are no longer being stolen. (The sky is a pretty blue now, but its unclear whether that's due to stopping the fumes from the rocket fuel, or just a symbol of the better situation for the island.)