Went to System Preferences>Security & Privacy>General>Unlocked>checked "require password after sleep immediately">relocked. Password is already in my system. After sleep, the screen requiring the password doesn't come up. I've done this same process on my other MBP, and it worked fine. I don't understand why it doesn't work on this MBP. Both MPBs have OS X 10.9.3. Since I posted this a few minutes ago, I found the "solution"...after doing what I wrote above, I restarted the system, and then the password screen appeared. Lots of stuff gets corrected with a restart.