Hi, CO!
Welcome to the forums! I am also a fan of the series since it began in the U.S. in 1998. :p I used to watch the show every time it on was on, too, I believe on the weekdays (with new episodes on Saturday), on the WB network! Good times, good times. I also was a collector of the cards and have thousands of them laying around! I've been on and off from the games, too, but I always seem to come back to relive the memories with the new games that are released. Pokémon is seriously one of those game series that you just cannot escape no matter what age you are.
& about your game! I'm sorry that happened to you! The feeling is mutual because it's happen to me before on my Silver version. I believe what you're experiencing is a "dead battery" in the cartridge, meaning just that, that your battery is dead and needs to be replaced if you want to be able to save the game file. You see, as the years go by, the battery becomes "dried out" from normal usage and also from things in the game (the clock in the game wears out the battery). I am pretty sure this is the issue you're facing, so I think you either have two options. You could manually replace the battery yourself, which I heard isn't
too difficult, although you do need to buy some cheap tools (like a soldering iron) and a new battery, which you may have laying around your house anyways, or you need to buy a completely new game (either used with a new battery, or a brand new one). Just to make sure that the dried out battery is the issue, you should still ask in the
Technology & Internet forum (link provided to you by Cirno). There are plenty of tutorials on YT on how to change the batteries from Pokémon games specifically, so you should check those out, too, if you decide to change the battery yourself.
Hope I helped, and hope to see you around!