On your laptop you have OEM license code Windows 7 Home Permium, and, most likely, you are trying to install Retail version of Windows 7 HP. OEM key will not work for retail OS. You have to either reach out to Asus and get Win7 they pre-install on their laptops, or call MS so they could try transfer your OEM key to Retail (rarely happens, I would not expect it to happen).
As it was simply put by one individual "The OEM version can only be used once on that system and no tech support from M.S. The RETAIL version can be installed in multiple computers, one at a time. Meaning you can install then deinstall then install in another computer. Plus you can call or email M.S. for tech support."