if its not getting any power light then its a power issue.
did anything happen suddenly before the old batteries die? any possible liquid damage?
might sound silly and i HATE to ask but are the batteries in the right polarity?
and youve obviously tried confirmed fresh batteries?
are they rechargeables ?
have you checked to make sure the contacts are extended enough for the negative to make a solid contact with the batteries?
any corrosion?
if youve checked all that you may need to open the mouse up and take some voltage readings and make sure the board is getting power. if it is then you have a bigger issue and will need further trouble shooting.