Anachronox/MysTech Tunnels

At the bottom of the elevator, look left for a Glodent. After the second fight, look right for a Batt. After the third fight, watch for a chest on your right with a TACO. After the fight with the Stare Bear, watch for the Vistin Spikehead (Grumpos, Poor, Melee) on your left as you go up the ramp.

At the junction past the bridge, turn left. After the fight, check out the Lifeflower by the wall. From now on, every time you pass a Lifeflower, pick a petal. They'll be useful later.

Head back to the junction and go the other way. When you reach the TimeMinder, save.

Sewagic Rapids Minigame
The object of this game is to pick up as many starred crates as you can without getting blown up. If you survive, you'll get a reward based on how many crates you grabbed:

Lower Tunnels
Grab the two HealGrease by the boxes. After the fight, grab the two HealGrease by the box. After a fight with 2 Stare Bears and 2 Mean Moles, watch out for a HealGrease Complete on the left. Save at the TimeMinder, and grab the HealGrease Complete on the left around the corner.

BOSS: Stone Sentinel
He always attacks the hexes in the same order, so you just need to make sure you aren't there when he does. A simple rule: when he attacks the space between Sly and Grumpos, move them away.

Continue on and grab the stone. Cutscene. Grumpos pays you $100, and you wind up back at the door, minus one Doorlord.

Head for Anachronox Tours, and the guy with the PAL-18. He'll sell you the battery now, so buy it. Now head back to your office, and wake up the little guy.