Sync isn't a backup system it sync between device to sync server back to devices. If you want to keep your data you must backup the data to restore to the new computer so they don't get lost. This is how you backup and restore your data back to new computer so they remain on the new computer. You need to search Firefox FAQ how to backup your data, bookmark, profile, login saves to files or USB and restore them back to the new computer so they remain on the new computer. If you don't do this sync will not keep data up to date as when you sync the new computer the old sync server data will be wiped clean and new data will take it's place rendering any previous data gone.

Hi Michael, do you have any access to your old computer (or just its hard drive/SSD), or a backup?