How to fix iCloud Password problem

I use iCloud to sync (among other things) my iCal on two MacBook Pros (both running 10.7.5) and my iPhone (running 7.0.2). A while back, the iPhone discussion let me solve the problem of duplicated appointments on my iPhone, but now I have a new problem. Beginning a few days ago, iCal on one of the Macs (the older of the two) started giving error message that my iCloud login/password information would not let iCal connect to iCloud. The only thing that has changed in the last month is upgrading iOS on the iPhone to iOS 7, and that was days before the problem appeared. I have used Keychain access to compare the iCloud passwords on both Macs and they are identical, as are the login names. Any ideas?