Prior to reading Myra J's post, "Internet Sharing" was the only box checked in "System Preferences"/"Sharing" on my mid 2011 iMac. "Security" was set to "None".
Result: the WiFi signal was recognizable, available and connectable. However, it failed to allow my iPad and Android phone to actually use the internet or any applications that use internet services. This was variable to some degree - sometimes it would work for a couple minutes and then cut out. Turning "Security" on to "WEP" made it worse, shortening the amount of time it worked.
After reading Myra J's post, I kept all "Internet Sharing" related settings the same as above and simply checked the following three boxes in "System Preferences"/"Sharing": "Sceen Sharing", "Scanner Sharing", "Web Sharing".
Result: the WiFi signal is working regularly now for about 12 hours.
Others experiencing these same problem should try simply checking these three boxes. Please report back with either:
"Checking Three More Boxes Allowed Internet Sharing to Work"
or
"Checking Three More Boxes Didn't Allow Internet Sharing to Work"
Looking forward to hearing from others...
Also looking forward to an update/fix from Apple that allows Security to be used again...