The university gave me a new lap top but my zotero libraries did not move to the new lap top - they have disappeared - they must be out there somewhere - can anyone tell me how to recover them?
See where it says "Web library" up top here on this page (on desktop)? Check if you're data is on there. If yes you can set up synching with your credentials and it'll be downloaded. See https://www.zotero.org/support/sync
Or if you never (fully) synced your library on the old computer online to Zotero servers, you would either need to do that now on the old computer (Option A below) or copy the data folder from your old computer (Option B): https://www.zotero.org/support/kb/transferring_a_library
Upgrade Storage
Check if you're data is on there.
If yes you can set up synching with your credentials and it'll be downloaded. See https://www.zotero.org/support/sync
https://www.zotero.org/support/kb/transferring_a_library