Magic Mouse green light doesn't work at all.

If the green light is not showing the batteries are not the right size, not connecting properly or the mouse is dead. Hoping the latter isn't true, let's deal with the batteries.

The batteries usually found best are Energiser, Eneloop, Duracell and Apple. Others have been found to be inconsistent in size (even a millimetre is enough) and that is particularly likely with fakes. Sometimes if you shake the mouse you can hear them move.

Then, if the batteries you replaced had leaked they could have left a deposit on the compartment contact points. Clean the compartment connection points thoroughly, then the battery's contact points, reinsert and try again.