Hey thanks for the report, couple of questions.

1. Are you updated to the latest version of Fortnite? v13.20. You can make sure you are updated by visiting the App store on your device.
2. What device are you on?
3. Do you have another device or platform that you are able to login on?
4. Have you tried these workarounds?

Workarounds
1) Reinstalling the game. If this does not work attempt workaround #2

2) Launch with the wifi and cell turned off, once you reach the no connection screen, then turn them back on and that might get you past the start up screen.