To start off, you need the Shiny Gyarados to do anything. Go back to Goldenrod city. You will find a whole bunch of team rocket members there. Enter the radio tower and you'll find a rocket member guarding the stairs, and won't let you through until you get a team rocket suit. Leave the radio tower then go to the underground passage in Goldenrod, in there you should find a Team Rocket member next to a camera. Read on.
Talk to him, and he'll give you a suit thinking you're a new recruit. Now go back to the guy in front of the stairs and he'll let you through. Now just beat the team rocket leaders/members and then you'll have access to Blackthorn City, going through the Ice Path.
To round off:
- Go to the Lake of Rage and defeat/capture Red Gyarados.
- Talk to Lance at the Lake of Rage.
- Head to the Mahogany store, and you will see a small cutscene leading to a secret stairway to a Team Rocket Hideout.
- Navigate and clear the Team Rocket hideout.
- Defeat the Mahogany Town gym leader.
- Return to Goldenrod City and defeat Team Rocket at the Radio Tower and at Goldenrod Underground.
Now, go to route 44, where you will lead on to the Ice Path and you will be able proceed on from there.