Did you restart the unit within 3 minutes after a power failure? If the power was off for less than 3 minutes, and you restarted the air conditioner within 3 minutes, a protective device may cause the compressor to shut off, preventing cooling for about 5 minutes.
Water will collect in the bottom tray of the unit. This is normal. Water condenses on the evaporator coil at the front of the unit and is channeled to the rear where it is picked up by the condenser fan. The water is blown onto the condenser coil fins and this creates a "splashing"...