Were you previously using Sync with the old computer ?

Can you still access the profile folder on the old hard drive if you use an enclosure to connect this drive via USB or is that drive completely dead ?

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

For the logins you need logins.json and key4.db.

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>

Old comp wont power on. Not sync'd with any other units.

The hard drive in the old computer may still be accessible but you need to install it to a case as an external drive or add it to your new computer. To do that and check the drive you probably need a technician. So, you have no backups?

If you have not turned on the syn on your old computer then the only way is suggested by @TerryN21. Connect the hard disk of the old computer and export all the bookmarks or locate the file "logins.json and key4.db".