The bad news is that your florist's cyclamen (Cyclamen persicum) was probably not dead when you tossed it. Cyclamen have a dormant season, not uncommon in bulbous plants. Technically, the bulblike structure in cyclamen is a corm, but whether it's a bulb, corm or rhizome, such a structure is meant to store energy for new growth. It's a strategy for surviving hard times, be they cold winters or hot, dry summers.
Cyclamen grows and blooms in winter. Once the days grow long and the temperatures warm, the plant goes into its resting phase. The foliage will begin to yellow, giving you the signal to stop watering. Once the foliage has withered, put the plant, pot and all, in a dark, dry, cool place. In the fall, report it in just a slightly larger pot and resume watering. Fertilize it once foliage is showing.
Though some see saving a cyclamen from year to year as too much trouble and purchase a new one each winter, simply putting a plant in a dark, dry place for the summer not take major effort.