Thanks for the advice. I could hear the click, but even when I reinstalled the battery, nothing would register. I also reset the computer unit and reentered the data.

For the past couple of days, I've used a Garmin GPS unit instead of a cycle computer. It's worked, but it also has its drawbacks. (Starting it up takes a little longer, the odometer doesn't register cumulative totals after I shut it down and then restart it and I'm constantly recharging the batteries.)

Tomorrow or the next day I'll be at the bike shop, preparing to replace the computer. I'm hoping the next bike computer will last me longer than this one has lasted.