You are correct, to use Desktop you need a license number. If TurboTax Online is not letting you continue, you can try the following:
Go out of your program and go back in.
Clear your cache and cookies.
Try a different Web Browser.
On the app: force-quit and reopen; update the app; restart your device; ensure storage and network are OK; try switching Wi-Fi/cellular.
If you have any additional questions or information regarding this please return to TurboTax Community and we would be glad to help.