I have a wireless mighty mouse, worked fine until I knocked it off my desk, after that it worked intermittently until it stopped altogether. Did a few google searches to find out how to take it apart, basically involves breaking the glued on seal to get in.
Once I'd got it apart the PCB inside is only seated on 4 plastic posts, not screwed down or clipped in. Mine had shifted a couple of mm up the posts because it must have landed upside down. This small movement was preventing the sliding switch from the battery cover engaging with the PCB. If I'd have known this before I may have not needed to take it apart, a few hard taps on a padded but firm surface may well have re-seated the PCB. Once I seated the board back into place and re-assembled it has worked perfectly ever since.
Not sure if this will apply to any of you because I know some are only a few days old but they may have had a knock in transportation? Anyway just thought I'd share my experience because I was having a hard time disposing of a £40+ mouse.