Possibly. Within that zotero folder, you should see files named: zotero.sqlite and zotero.sqlite.bak and you may see additional files named, e.g. zotero.sqlite.1.bak.
These are the database and database backup files.
Please provide the names, dates, and sizes of these files.
With firefox closed, you can make backup copies of these.
On old computer, with Firefox closed, copy the entire zotero directory to your external drive
On new computer, find your zotero data directory.
Decide what you want to happen with any references you've added on the new computer. If you want to keep them, then backup your zotero data directory & also enable syncing. If you haven't added anything important, proceed.
With Firefox closed on your new computer, copy zotero.sqlite and the storage directory to a temporary directory on your desktop.
Now copy the storage directory and zotero.sqlite from your old desktop that you stored on the external hard drive to your zotero directory on the new computer.
Relaunch firefox to verify Zotero is working with your old library
Now setup syncing and backups to your external drive so you don't run into this scare again.
i last added to the library in May. I have been focusing on data analysis in spss since then. I have to leave in about five minutes. why is zotero not recognizing my library? Or is that a whole other thread?
More investigation would probably lead to an answer. This can happen if you creates a new user account in Windows, created a new profile in Firefox (which can happen if you've updated Firefox or use their reset function, described above), or modified the setting that specifies where zotero data is stored.
Upgrade Storage
These are the database and database backup files.
Please provide the names, dates, and sizes of these files.
With firefox closed, you can make backup copies of these.
zotero.sqlite.1.bak - 5/15/16 9:03 am - BAK File - 1892 KB
zotero.sqlite.bak - 5/21/16 8:42 am - BAK File - 1860 KB