I actually have about 9 hours more playtime on Silver than I do on Gold (105 hours on Silver, 96 on Gold). Overall, I've done more soft resets on Silver as well, as getting shiny Ho-Oh on Gold only took 107 soft resets, while Lugia on Silver took 12,000+ soft resets. While I was hunting Lugia, I didn't use Gold at all. Finally, I've been using both games at the same time to hatch shinnies from eggs, that's where around 3/5 of the playtime in my games are invested in. Both games have all 16 badges, I still gotta fight Red though.
Gold's ID: 04735
With this info (I just now double checked, so it's correct), I get the generated password 00731. I try to enter this password, and it doesn't accept it. I have all of my shinnies on Silver right now, so if I lose Gold now I'll be fine, but I don't understand why it's dying so soon, batteries should last 5 or so years...