I found a PDF copy of the user manual online (66 pages) and have stashed it here for future reference.

It can be activated out of the water by wetting your fingers and touching both "COM" and "PLAN ON", once activated you can roam through various modes by touching the three contacts ("COM", "PLAN ON" and "TIME MODE") in various ways.

The battery is a 3 volt lithium CR 1/2 AA unit. There is all kinds of confusion about what battery you can use for the replacement (being that lithium CR 1/2 AA batteries can be obtained in both 3.0 and 3.6 volt versions). The original battery is a 3.0 volt varta and you definitely will not go wrong replacing the battery with one of these. You also need to install a new O-ring when you replace the battery. What I did in 2012 was to find a replacement kit which includes the battery, O-ring, some silicone grease, and a bunch of other O-rings (so you could replace every O-ring in the unit should you want to). I bought this on Ebay for just under $20 including shipping - the kit includes the Varta battery. I saw a report from someone online who replaced the battery with a 3.6 volt version and said that the computer "seemed to be working fine", but I am uneasy about this and feel it is safest and wisest to do the replacement with the exact battery originally used.

To replace the battery, the game goes like this:

• Be sure the unit is dry and clean.
• Remove backplate by loosening 4 phillips screws. (The back of the unit boldly proclaims "do not remove screws")
• Remove battery compartment cover, carefully place it with sealing surface up and keep it clean.
• Remove and dispose of O-ring even if it looks fine.
• Lift battery carefully, beginning with positive end, but keeping the battery horizontal, avoiding prying force.
• Inspect battery, contacts, and housing for moisture, corrosion, and such.
• Install new battery with care as to polarity (reversing polarity will clear calibration data and require a return to factory), do not touch contacts.
• Touch COM and MODE/TIME to start the computer. Ensure that it displays a depth of zero.
• If it does not start with zero depth displayed, remove battery, wait a minute, reinsert batter, wait an hour, then restart computer, do not touch contacts during the hour.
• Install new O-ring with thin film of pure silicone grease. It should be shiny with no visible grease.
• Gently place battery cover in place, but do not push down on it yet.
• Put your thumb through the backplate hole and push the battery cover into place. Maintain pressure and check that the O-ring has not extruded out. Maintain pressure as you tighten the four screws. Tighten in a criss-cross pattern, not one screw all at once. Only a snug fit is required, do not overtighten.
• Make a final check that the batter compartment is in place and that the O-ring has not extruded.