Do you still have your old machine? You can migrate your old profile over to your new computer without too much trouble or you can export your bookmarks very easily.

Unfortunately, there is no way to recover a lost Sync account without the password or email access. https://support.mozilla.org/en-US/kb/ive-lost-my-firefox-sync-account-information#w_iaove-forgotten-or-dont-have-access-to-my-firefox-account-email-address

I received a private message asking how to export bookmarks and passwords. Here was my response for the benefit of future readers:

Here are instructions for exporting bookmarks: https://support.mozilla.org/en-US/kb/export-firefox-bookmarks-to-backup-or-transfer

If you want your passwords also, you're probably better off exporting your entire profile. https://support.mozilla.org/en-US/kb/back-and-restore-information-firefox-profiles