Asus K75D windows 8, install windows 7
Solution 1:
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I cannot comment on that, but if it is a 25 digit alphanumeric key, then it most probably is your product key or serial key. You can confirm, by going to:
Control Panel>System and Security>Action Center>Security>View activation details (Under Windows Activation) --If you are on Category view on the Control Panel
Control Panel>Action Center>Security>View activation details (Under Windows Activation) --If you are on Large/Small icons view on the Control Panel
This will give the last 5 digits of the key and you can check the last five digits on the BIOS to confirm
No you cannot use the Windows 8 key on Windows 7. But if you really want to downgrade, some laptops have downgrade rights. Read here and here to get a better understanding.
I don't really understand where the question is, but yes, only 3rd party apps can bring back the Start menu at the moment. If you end up wanting to use a 3rd party app, try Pokki, which is amazing, or some of the other suggestions here
Solution 2:
Without having Windows 8 Pro installed you have no rights to a licence for Windows 7. Businesses are more likely to have a valid reason to downgrade than home users, and are also likely to have "site" licences that would cover the downgrade so them doing so is not going to be a problem to Microsoft.
As a home user you most likely have Windows 8 Home Premium and so have no rights to downgrade your licence. Your Windows 8 licence will almost certainly not work with Windows 7.
In order to downgrade you would have to purchase a valid Windows 7 licence.