If the desktops and laptops used 100% identical hardware and 100% identical bioses then I would be wondering why desktops work and laptops don't.
However, the fact is that desktops and laptops have substantial hardware differences due to the power available to drive the hardware - ie mains v battery. So it is likely that both the bioses and the chipsets are different and therefore there may also be differences in the drivers required as different memory and IO port locations may be used to interface with the chipset.
So it's really up to you to determine which drivers WILL work on your laptop hardware. Good luck!