Fuel Pump

No, the relay wouldn't make it hum. Are you still having starting problems? Was the new pump from a Chevy dealer or an aftermarket pump. Some pumps are just loud. I found complaints from other people with loud pumps but they were usually on Chevy trucks. I would check your fuel pressure and make sure it's where it should be. You may just be stuck with a noisy pump. Are you sure it's the pump though. Turn the key to run (engine off), listen, the pump should come on for 2 seconds and shut off. Is this the same sound you hear? Listen at the tank with the cap off while someone else turns the key to run. Just saying, make sure it's the pump. You may just have a noisy pump. Save your receipt if it's under warranty. The new pump could possibly be defective.