Usually the pump cycling like that indicates a leak. If all the connections you checked are dry, then it's likely a suction side leak such that the leak can suck air but oozes no water. Pressure side leaks are always wet.
Hope you find it. Usually there aren't too many suction side joints. I'd try disassembling and resealing each connection on that side of the pump. Sometimes Teflon tape doesn't cut it on plastic threads so I'd try a paste type joint compound. Sometimes the 'hand tight' plastic connections need a little help from the channel locks. An extra 1/4 turn on the right fitting may solve the problem.:)
