does the battery pilot lamp light up when you switch on ignition?
I don't think, that the hydraulic pump is the cause, it's obviously the consequence.
What makes you sure that the aux-belt is tensioned seriously? It doesn't mean anything, if you can't hear it squealing, especially when the belt and pulleys are wet.
I guess it is a matter of drive belt tensioning or it's condition. The temporarily break down of the power steering is an unambiguously sign.
