For some reason, our basement is not draining. We have replaced the sump pump, but there is still water coming in. Could the underneath be clogged in some way, and if so, how do we correct it?

This could be a problem from the outside not the inside. Have you checked your gutters to see if they are properly channeling the water away from the foundation? Have you had any recent landscaping around your home to where the dirt has been added in one area? This was the exact problem we had with a customer's home that kept getting water into it. The customer had extensive landscaping done and altered the original basement/dirt configuration from when the home was built.