Pardon me for butting in........
"because it was made very clear that the key should stay in the Bios..."
You have been misinformed or you have misinterpreted the information.
The info applies ONLY to Win 8 or 8.1 pre-installed in the computer.
Your computer was preinstalled with Win 7.
I don't know if you can still do this........ If you can login, google for Belarc Advisor or Produkey.
Hopefully, either one will give you your win8/8.1 product key.