If the computer was original sold with Windows 8 (the BIOS date may be an indicator) then the key will be embedded into the BIOS. Installing from a Windows 8.1 DVD and choosing the option to enter a key later may allow Windows to pick up the license state from the BIOS so some time after the install it shows up as licensed. However which particular version would require some trial and error
If supplied with Windows 7 it should have an OEM license sticker underneath or it could be in the battery bay. It may be possible to get more information from the manufacturer.