The clock uses very little power so a weak supply might still be able to provide stable voltage to it.
All the other functions require enough power to drag down a supply that is on its last legs and I think that is where the problem lays.
If the display brightness seems normal, then either a different section is being used for the missing functions or a weak capacitor in the power supply can no longer filter the DC voltage well enough to provide stable voltage to motors, the main board, etc.
To determine what is at fault will require some technical skills and a couple of instruments normally not found at home.
About the only thing you might try on your own is to open the case, look for a customarily separate board that appears related to the AC input cord which should be unplugged at this time.
You will see cylindrical parts ranging in diameter from 1/4" to about 1 1/4" and various heights.
The tops are normally visible and the cases are of aluminum. Look for any that seem to have bulging tops or a crusty deposit around their base.
Those things are visible indicators of failure.
If you find such parts and have an appropriate soldering iron (not a higher power 'gun') you might remove these and buy replacements.
That could be a problem since most electronics supply places won't even talk to you.
If you want to try on line, look at www.mouser.com
, one of the few who will sell single quantities of parts.
The values will look something like this:
These parts are polarized so if you don't see a '+' or '-' on the board, be sure to mark it before removing so any new part does not fail immediately after replacing.