If big things were made the same way as small things, they would be prohibitively expensive and inefficient. Making pumps that could function in a flooded city would certainly have been possible (simplest method being to build a waterproof wall around the pumping station, and using a small pump to keep it dry).
The bigger question, though, is what would be the purpose of spending even $10,000/pump on such an improvement? If the pumps are able to withstand a moderate rise in water level, a flood beyond that would suggest one thing: a breached levee. And if that happens, it doesn't matter whether the pumps are working or not.
Simply put: once a levy is breached, there is no possible amount of pumping that will prevent the waters on both sides from reaching equilibrium. Even if one had enough pumps to remove a foot of water per minute (that's 720 times what the NO pumps could do if working) it wouldn't take very many days before the levees were letting through more than that.
Nightline: The prison riot and hostage rumor was false.
"Power has got to be the problem." Well, sorta. My understanding is that the emergency generators for the pumps are in sheds that were destroyed. Getting to them, getting them up & running should not be a long-term project, just a repair job.