You'll notice that it moves back and forth several times. Press the cartridge button again to restore it to its normal operating position.
Carefully replace the lid by slipping it back under the tabs on the top of the tank. Then use a Q-tip to soak up the excess ink inside the tank, which is made of a rubbery material. Then use a small knife blade or screwdriver tip to remove the tank lid. If you just want to clean the waste ink tank, use a Q-tip to clean the visible gunk. To move the carriage aside, follow Russ Wright's procedure to reset the waste counter, then you can press the cartridge button and the carriage will move to the center. It'll be above the waste ink tank, which will be hidden from view. Turn the printer rightside up with the front facing you and you'll see the print carriage on the right. When they're both free, the remaining tabs act like a hinge, so you can remove the cover entirely. Once you feel the first tab loosen, move on the second one. The cover is held on by four plastic tabs, so use the screwdriver to pry a tab toward the middle of the printer while you gently pull the cover apart. Disconnect the power, turn the printer upside down, remove the screw, then carefully insert a small flat screwdriver into a slot. Your intuition about the slots is correct.
