Hi,

just transfer your entire firefox profile to your new computer via your external HDD. (That transfer cable is a ripp-off btw.)
On your old computer klick Start -> Run, then type "%appdata%" (without the quotation marks)
Then you should have a new explorer Window with some folders. There should be a folder "mozilla" with subfolder "Firefox". Open the Firefox folder and copy its contents to a folder on your external HDD.

Now go to your new computer, there you do the same, until you have your Firefox folder. Backup its content in case something goes wrong. Then delete all files and folders and copy the files and folders from your external HDD to this place.

Michael