You don't go in that cave, in fact if you see a team galactic guy blocking a cave entrance and saying he does not have a Pokemon you:
1) Laugh at him.
2) Get out of that room! There is another seceret cave in the previous room in the top left part of the room.
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u catch girantina and then after that you go to veilstone city and go talk to the team galactic person in front of the galactic warehouse I think galactic warehouse it is one on the team galactic places in veilstone city and then he will go somewhere and drop a key which it will be the storage key. Hope this helped and sorry I cant think of the name of the team galactic place it is the biggest building of the team galactic places (in veilstone city)
To find the Galactic HQ special key, you first need to fight Team Galactic at the three lakes. The last one being Lake Acruity which is blocked by some Grunts until you aquire the icile badge. Once this is done and you return to the HQ, there will be a grunt outside looking at a satellite dish talking to himself, approach him and he will run away dropping a galactic key :)
it is easy all you have to do is go through Mt. coronet when you get outside to the snow you'll see rock climbing walls (you need HM rock climb) you will see caves but just pass them, after you climb all rock walls you will see one cave enter it . After entering the cave you will fight team galactic then at the end of the cave you will find Palkia.that will be the peak.
You can talk to a man in Veilistone city. His house is the first one to the left of the team galactic building.
you have to defeat team galactic in veilstone city. In their warehouse you can find the hm fly. You have to defeat gym leader maylene in veilstone city to use it. And you have to learn it to one of your Pokemon of course