I have a K501UW and can confirm that the issue is not in BIOS setup. I run both Win7 and Linux on the same machine. Touchpad works on linux and not on Win7.
I have also tried various drivers and various versions of the same driver with no success. My guess is that the only drivers ever made for this hardware is for windows 8 and up, and no one ever bothered to make a driver for windows 7.
What about ATK package? I installed it and all the FN keys...
Have you had any luck fixing the toutchpad?
I have the exact same problem on an K501UW after downgrading to windows 7. I also run linux on the same machine and the touchpad works. I can confirm that it is an ELAN.