Hi there I recently got a new laptop and all of the flashcards that I made on my old laptop on anki desktop do not appear to have transferred across. Is there any way that I can pull the flashcards from my old laptop onto ankiweb so that I can see them all on my new laptop? To make things worse I do not have access to the old laptop anymore so can this be done remotely? 
That’s how the ankiweb sync should work. Push up from one device and sync back in to your new laptop using the same account. Or then worst case export the decks as files and re-import. But sync is much easier.
If you don’t have access to the old laptop, and had not synced it before you lost access, I’m afraid there is no way to recover the data.
I wish new users would
a) learn how ankiweb syncs and do that every time they use the apps
b) learn how to export anki decks to local file system and even better to remote backups just in case.
Maybe we need something in the UI that enforces the usage pattern for anyone who opens the app the first time on a device. Would it be too much if the first-time app start would include a dialog box to create an ankiweb account as a gentle reminder?