My TI-89 Calculator will not turn on. I have changed the batteries with no result. The calculator was damaged while it was in the possession of my brother, thus I do not know what is wrong with it. When I took the batteries out to replace them, however, there was accumulated corrosion.....water damage, maybe? Thoughts?

The damage was battery corrosion. If you CAREFULLY take a damp(not dripping wet) rag and wipe the contacts of the corrosion you may have luck. The batteries just leaked, Very common especially for cheap "Heavy Duty" batteries. Alkalines seem to hold up better in a discharged condition. I hope this helps.Do wash your hands after the cleaning. A q-tip may also be of help. Just wet it and squeeze most of the water from it.

I'm a chemist and have frequently seen battery leakage when battery-operated systems are stored too long. Try a que tip soaked in vinegar (a mild organic acid) to swab the corrosion and surrounding contacts. Neutralize the acid with a weak solution of baking soda, sodium bicarbonate. Dry residue with a clean swab.Water may (or may not) dissolve the corrosion, but residues must be removed with a dry swab.