The pump should be easily removed by simply pulling it from the tank. It can then be inspected more closely for blockage and the inlet and outlet poked with perhaps a cocktail stick.
When my tank showed evidence of blackness, I removed it and threw in a good handful of clean gravel, then 1/4 filled with water and gave it a good swirl. Once looking clean after several repeats, let it soak in a dilute white vinegar solution to kill off any remaining spores..
