The old generations of Pokemon used a save battery that could last from 10 to 20 years (maybe more, maybe less) depending on how it was used. The same thing happened to me a few months ago. However, there are videos on YouTube that detail how to replace the battery if you want to play them again.

My Silver battery just died too. Sucks. In other news, GB Sounds is the best key item ever.

I like the radio station that plays the classic stuff on Sundays

Team Rate:
I'll add a lot more details later, but just a few comments...
Power Gem sucks on Ampharos, because STAB T-Bolt does almost the exact same damage as a SE Power Gem, and the only time that won't be true is if you use PG on Volcarona, but that's a different game entirely. Consider replacing it with Focus Punch/Blast for more coverage.
Rock Slide on Magcargo's useless when Ancient Power does the same job, but a little better due to his higher Sp. Att, and better special effect (nothing will flinch).
Too many redundant moves on your Umbreon, and with his low attacking stats, you definitely don't need more than one of the same type attack. Personally, I like Payback, since it plays well with Umbreon's low speed, but consider putting Curse on it to make better use of the attack. Since it has Synchronize, you could use it to put random status on opponents, and give it rest to heal off the damage. Maybe Facade could also be used to play off the boosts and the ailment bit.
Yanmega needs to gain a few more levels to get his better moves Air Slash and Bug Buzz, I suggest you train yours more. Also, get rid of Ancient Power, Air Slash and Bug Buzz will do more damage generally.
I like your Mamoswine, consider using Curse over Rock Slide just to beef up the defense and make Avalanche and Ice Shard more worthwhile.

I'm going to replace Power Gem with Focus Blast. I didn't even realize it was readily available. A fighting move will be useful.

Magcargo is now 61 and has Flamethrower and Stealth Rocks instead of Lava Plume and Rock Slide.

Facade and Rest might be really cool for Umbreon, though I'm leaning towards just using Mamoswine instead. I thought Curse was only available as an egg move. Can egg moves be taught at the move tutor?

For Yanmega, do you suggest dropping both Silver Wind and Ancient Power for Bug Buzz and Air Slash? I like the 10% chance of a stat increase on those moves, but it rarely procs. Or should I drop Shadow Ball or Giga Drain? I like the added type coverage but there's no STAB and all that stuff.

Awesome.

Better as well.

You're right, it is only an egg move; forgot that HGSS doesn't have a TM for Curse like the original games, nor a move tutor for it. It should've been more widespread and available. I guess forget my mentions for Curse, unless you don't mind doing the extra work to breed it on.

The thing you have to consider when battling is that sometimes it's best to just go for the win as opposed to the chance that you might get a super boost. 10% isn't high probability for anything, especially for something as frail as Yanmega who might not live to take advantage of the boost, let alone see it happen. You shouldn't teach weak attacks just for tiny possibilities like that, it's the equivalent to teaching Mewtwo Confusion for the 10% of confusion.
Including STAB, 90 BP isn't very damaging, while Bug Buzz has 135 BP and can lower your opponent's Sp. Def with the same chance as Silver Wind can boost all your stats. Raising your stats is cool, but doing high damage is invaluable.
Air Slash has a 28.5% chance of making your opponent flinch and not hit you at all, which Yanmega can abuse very well given its Speed. Also, like I said, Yanmega's frail; any turn it doesn't take damage is good for you.
Back to damage output, Air Slash has 113 BP with STAB, compared to a super effective AP (120 BP). You're not missing out on much for coverage, and you have almost 3 times the chance of something beneficial happening to you when you choose Air Slash over Ancient Power.
I can see the use in Giga Drain because of the potential to do a lot of damage to the various Rock/Ground, Rock/Water, and Water/Ground types, along with the recovery provided, so even though it is 60 BP, more often than not the attack'll benefit you. Shadow Ball's redundant with Bug Buzz though, since Ghost is only useful on Ghosts and Psychic types, while Insect is good for Plants, Psychics and Darks. Also, if you're going for just neutral damage, Bug Buzz will win out, especially since you have a poke with Stealth Rock on your team to give that regular damage.
I definitely suggest getting rid of SW and AP for Air Slash and Bug Buzz. As for Giga Drain and Shadow Ball, I'd choose to keep Giga Drain, and maybe replace Shadow Ball with something else. It does learn Detect, that'd be great to ensure you don't take any damage and you get one speed boost bonus right away.

You mean a battery inside the actual game cartridge itself? Weird but thanks i'll look that up.

Took your advice with Yanmega and he doesn't suck anymore. Is it worth having both Flamethrower and Fire Blast on Magcargo? I was going to give him Sandstorm once I realized it boosts his Sp. Def. by 50%, but then I remembered I sold the TM. :|

Also, the fact that you need Rock Climb to get to Red totally blows. BLOWS. I suppose I could give it to Mamoswine in place of Rock Slide.

Yeah, some NES games had an internal battery to keep track of saved date as well (Like the first two Legend of Zelda titles), I suppose it has something to do with the way data was stored on the cartridges, but I can't be certain.

NES, SNES and some N64 games had them, I thought. Might be wrong about N64. But I've got a dead copy of Pokemon Silver and a dead copy of EarthBound waiting for new batteries.

I think some did, but there was also that Save Pak thing that could plug into the controller and that'd work

Why does Gamefreak obligate us to put HMs on our mains to finish the game?! Thankfully, Ice and Ground get great coverage together, so Mamoswine can handle losing Rock Slide, though it is a shame to lose it to Rock Climb...
As for Magcargo, Fire Blast or Flamethrower, you don't need both. It's a toss up on this one, and it comes down to whether you want more reliable accuracy or more power. In either case, replace the other attack with Recover to give the little snail some staying power. Good thing that all you need is a Heart Scale (they have those in HGSS, right?).
Anyway, more rates! Quagsire's set's alright, wish it didn't have to be bred to get Recover and Curse, as those are terrific moves for the bulky bastard. I'm not a fan of running both Surf and Waterfall, but I can see some value in Surf for the Sp. Def weak Rock/Ground types (namely, all of them).
You got a Modest Xatu? Exploit that Special Attack boost and forget Fly. My opinion on Ominus Wind's the same as it is for Silver Wind and Ancient Power on Yanmega, especially since the bird has access to one of the best boosting moves in this game, Calm Mind. Replace Fly with Calm Mind (STAB be damned, as it doesn't learn any special Flying attacks), and replace OW with the better move Heat Wave. Fire attacks cover nearly everything that Flying would (with the exception of Fighting, but that's what Psychic's for), and Heat Wave can also take out Steel types, which would otherwise wall you. Grass Knot's great for doing between 80 and 120 damage to the likes of Tyranitar, Rhyperior, Suicune, and any other heavy bastard in the game (basically the majority of fully-evolved pokemon), but if you want some reliable damage and recovery, consider Roost and using Life Orb over Wise Glasses.

Recover sounds good, I'll probably drop Fire Blast. I seem to have terrible luck with accuracy. Time to go smash rocks for an hour.

Surf and Fly I'm only really keeping around for out of battle use, so I can drop those. Would Yawn be good to use for Quagsire?

I don't really have any idea how the Battle Frontier works. How long does it take to get 48BP for a TM?

Yes it would. I think that Haze would be worth replacing for that one, since there are better, bulkier Hazers in the game that you could use. You could also run Toxic.

Unfortunately, a very long time. The moves are worth it, but it'll take a lot of battling. On the plus side, if you get high win streaks, you'll be challenged by the Frontier Brains and get 20 BPs for beating them.

Hidden Silver version.