The problem is likely on the game cartridge itself, since the game cartridge is the component that holds the SRAM memory (used for saving the game data), as well as the internal battery that is the power source for the game's ability to write the save data to the SRAM. Most hardware problems will be in either of those two components, which will mean your game won't work.
To check if your HGSS file works without "resuming" the actual file, go to the Pokéwalker menu and see if you can access more than one route (NOTE: if you've never used the Walker before, you've likely not unlocked any more than one or two? routes) and then if you can see all of your Pokémon (in your party and in your boxes).