Can you access the old drive?

https://support.mozilla.org/en-US/kb/how-run-firefox-when-profile-missing-inaccessible

http://kb.mozillazine.org/Profile_folder_-_Firefox#Navigating_to_the_profile_folder

https://support.mozilla.org/en-US/kb/profile-manager-create-and-remove-firefox-profiles

https://support.mozilla.org/en-US/kb/back-and-restore-information-firefox-profiles

Firefox uses two locations for the Firefox profile folder, so make sure to look in the correct location.

Location used for the main profile that keeps your personal data (Root Directory on about:profiles).

• C:\Users\<user>\AppData\Roaming\Mozilla\Firefox\Profiles\<profile>\

You can copy specific files with Firefox closed to the current profile folder to transfer/recover personal data. Note that best is to avoid copying a full profile folder.

• https://support.mozilla.org/en-US/kb/recovering-important-data-from-an-old-profile

• bookmarks and history: places.sqlite
• favicons: favicons.sqlite
• bookmark backups: compressed .jsonlz4 JSON backups in the bookmarkbackups folder
• cookies.sqlite for the Cookies
• formhistory.sqlite for saved autocomplete Form Data
• logins.json (passwords) and key4.db (58+) or key3.db (57 and older) (decryption key) for Passwords saved in the Password Manager
  if you only have key3.db then make sure to remove an existing key4.db
• cert9.db (58+) or cert8.db (57 and older) for (intermediate) certificates stored in the Certificate Manager
  if you only have cert8.db then make sure to remove an existing cert9.db
• persdict.dat for words you added to the spelling checker dictionary
• permissions.sqlite for Permissions and possibly content-prefs.sqlite for other website specific data (Site Preferences)
• sessionstore.jsonlz4 for open tabs and pinned tabs (see also the sessionstore-backups folder)