Hi,
Very strange you did not find the flash file on FS site. Look for exactly name of your laptop, you should find it on the list. Another option but not recommended (use it as the last thing)is to go on your mainboard manufacturer and download your file according with your type, sn, model of motherboard.
As you have the bios chip soldered will make a little bit more difficult to replace it but not impossible. Check this out:
www.recoverybios.com
*of course if you are still eligible/or not for free FS support you can try there first