One possibility is that the pump outlet check-valve is blocked. The pump outlet is the piece where the vinyl outflow tubing is connected in the picture below. (Sorry for the poor picture quality - all I had at the time was an old flip-phone.)
Disconnect the hose from the outlet:
Remove (unscrew) that barbed nipple that sticks out:
When you've removed the barbed nipple from the outlet, you'll see a rubber piece inside the bottom of it; that's the check valve:
Slide the check valve out from the hose nipple:
And clean out any crud inside the check valve; mine had a pretty solid plug of gunk in it which was blocking any outflow causing the alarm light to turn on:
Now just reassemble and the pump should function properly.
Note: If this valve clogged once, it WILL clog again. I have a very short vertical run of output tubing before dumping overboard (about 1 foot), and I reassembled my unit without the check valve and everything's fine. For significantly longer vertical runs of outlet tubing before it dumps overboard, you'll have all the condensate in that vertical run draining back into the pump reservoir when the pump shuts off if you don't use the check valve - this could cause the pump to short cycle. Also, if there is a possibility of external water siphoning back into the pump reservoir, you'll have to re-install the check valve - but at least you'll know what to do next time it clogs.