I understand your problem, but it is probably not the battery. I have purchased 4 different chargers/leads for my nuvi 2599 and none of them will charge it, but the original supplied leads and charger work fine. This seems to be a common problem with the 2599 ltd Many sellers say that their leads work with this satnav; but they do not. There is something peculiar about this model that means ordinary cables from many suppliers will not support the charging function and in some cases will not work properly with a computer to download updates. Before you spend money on a new battery make quite sure that it is not the cable you are using is not at fault.
Robert.