That won't be possible since the old computer no longer has access to it. What should've done was use the Firefox help tips to backup/import the profile and bookmarks and sessions and then import those back into the new computer and Firefox setup. That way insure all the data is up to date and none is missing. And as your old computer is died there nothing that can be done to move those data off since your not using the Browser to backup those data to transfer them. You need to at this point have computer shop see what they can do to get those data otherwise there not much more that can be done here.