Sounds like the sound a dead/dying battery makes, but you changed the battery. Clean the battery cable connections to the battery then clean the attachment points, especially the ground lead (should be on the engine block, not sure where on your car - follow the cable). Could likely be a build up of corrosion preventing the electrical power from making the circuit.
'73 280SEL 4.5 (9/72)- RIP
Only 8,173 units built from 5/71 thru 11/72
'02 CLK320 Cabriolet - wifey's mid-life crisis
2012 VW Jetta Sportwagon TDI...at least its a diesel
Non illegitemae carborundum.