I have a kidde nighthawk*(combo smoke/co alarm). It beeps about every 20 seconds with or without a good battery installed.

Does the display read, "Err"? According to the Kidde web site, all of their detectors (CO anyway, not sure about smoke) manufactured since, I believe, 2002, have a built-in clock that AUTOMATICALLY and apparently irreversibly disables them ~7 years after they are first powered up, a nice little "planned obsolescence/End-of-Life", under-documented "feature" that forces you to buy a replacement. Try to find THAT warning on the OUTSIDE of the packaging. Or call their "Hotline" at 1-800-880-6788 and tell them how you feel about it. If yours was manufactured before 2002 it may have escaped the automatic shut-down fate, so it probably really IS malfunctioning. Don't take a chance, just replace it.