I would take the drive belt off by undoing 4 x 7/16 bolts on the pulley, and then turn the pump backwards and forwards slowly by hand to see if it feels free, or grates, or is siezed.
I have replaced 4 in the last 2 months while rebuilding 4 engines. You need the head off to do it properly, so ideally the engine would need to come out, or you cannot get to the chain and cam sprockets which need to come off to get the head off.
If the pump feels free and turns easily, the only thing else that can go wrong is it can leak, and this can only be found out when the engine is up to temperature, and the cooling system is pressurised.
If all is well, I would drain the whole cooling system, flush it all through a few times, and then fill it with about 2 pints of antifreeze and clean water.