I just changed my starboard battrey because the old one will no longer hold a charge. When I connected the new battery, the bilge pump started humming and the bilge pump toggle switch lit up in the off position. When I pushed the switch to the on position the light remains on and the bilge pump gets louder and believe it or not the radio turns on

. All this with the battery switch in the off position. My radio has never turned on with the batteries off, even when I try to turn it on!! When I turn the battery switch on to the #1 (the starboard battery, the new one) the problem continues. If I turn on only the #2 battery the port one the problem is still the same. I have to disconnect the new battery for everything to go back to normal. The bilge switch only lights up in the on position and the bilge turns on like normal and the radio stays off.
I haven't had any work done on the boat. All the electronics were installed by the Pro Line dealer in 2008 when I purchased the boat new, including the radio. Everything was working fine two weeks ago with the old battery. The only thing I did was swap the old battery with a new one. What is going on? I can't believe that an electrical problem as odd as this can just start out of the blue. Can it be just a bad Bilge Pump that will make the electrial system act so hay wire??