Firefox only stores the bookmarks on your computer.

The only way Mozilla will store your bookmarks on their servers is if you have used the Firefox Sync extension, and if you did you would need to know your account details to retrieve them.

@TonyE

Okay - I never used the extension, but good to know. Would that mean that I could access bookmarks wherever?

Thank you for clearing that up. I guess I'm out of luck!

The Firefox Sync add-on is mainly used to synchronize bookmarks, passwords, history, open tabs and some preference between different computers. It can also be used if you have a new computer to download all of the data on the Firefox Sync servers onto the new computer, which effectively works like an online backup of your data. For more details on using it see https://support.mozilla.com/kb/what-firefox-sync

Firefox Sync doesn't allow you actually access your bookmarks from anywhere and view them on-line (like other bookmark sync services might), but you can sync a new Firefox installation from the sync server with the proper credentials or sync multiple PC's with with sync server so that all your PC's have the same bookmarks (and certain other types of Firefox data).

If you are replacing that old, crashed computer, you might be able to access all your stored data if you mount the old hard drive in a USB Enclosure and plug it into the new PC as an external drive.
https://support.mozilla.com/en-US/kb/Recovering+important+data+from+an+old+profile

Your old Profile is located here in Win XP and W2K:
drive:\Documents and Settings\Windows login user name\Application Data\Mozilla\Firefox\Profiles\profile_name

@the-edmeister

Thank you for your help. I actually have all been able to extract all of my data from my old hard drive (via USB Enclosure saved to an external) and so I have my data secured.

My OS on my old computer was Win Vista. When I go to AppData\Local\Mozilla\Firefox\Profiles\"profile name" there are two folder: Cache and Offline Cache. In the Cache folder, there are are bunch of files, and apparently the file type is "file". Also, in the profile folder there are three single files, two of which are MFL and one is SQLITE. Do you know what this means?

Sorry, you posted here the first time with WinXP so I falsely assumed the old one was WinXP, too. Wrong set of folders but close, you want the \AppData\Mozilla\Firefox path, not the \Local\ path.

@the-edmeister

Okay, I found the correct files but they are saved as JSON. Do you know which type of application can open this? I could not seem to figure it out.

Bookmarks > Organize Bookmarks -> Import & Backup - Restore - Choose File...

Thank you so much! That worked. :)

You're welcome.

@the-edmeister

I’m having similar problem. My old hard drive is now connected via USB port to my laptop as an external drive. The old hard drive was previously running on WinXP while my laptop is using Win7. I followed your instruction to restore the old data (bookmarks) ie. drive:\Documents and Settings\Windows login user name\Application Data\Mozilla\Firefox path. However, after I accessed the folder: Windows login user name, I could not find the folder named: Application Data. What have I missed here?

eden.