I am kinda confused, you did get the game but you don't have a gamegear, and only could try it in your friends gamegear?
there is no region lock, so if you had for example an american gg and a japan game, it should work fine
open it up and show us pictures of the pcb, can be a fake, can be bad contacts, or damage inside from previous owner...
there seems to be a lock chip like the nes\snes games, which is usually the reason of problems when theese games age...
however search in the internet for how to open it up, i think there is a security screw and some clips holding the cart, you might want to check on that before damaging the clips
if you only tried in 1 game gear, it can be that console problem
hey there is a everdrive for game gear, maybe you can look into that if you have a gamegear and don't want to deal with carts..