Generally just contact the OEM and they will sell you a simple OS install CD, usually like $9.99. Of course if you had created the DVD's when you purchased your computer, just restart them.
Both HP and DELL have this kind of a set up and their systems don't require a key. It may be embedded in the OS, but it probably knows upon installation what the manufacturer of the system is that you are installing on. Some of this may no longer be valid as I have not had to re-install a Windows 7 system on an OEM.
BTW-Dell uses the phrase "Recovery Disk", which sounds like what you are referring to. On some of the Dells I have worked on, that is the Windows OS. If you have a friend with a DELL OS or Recovery disk, you can legally install from their system since it checks the laptops chipset to ensure you are running a real Dell computer, given that you both own the same version of Windows.
Don't forget, create the DVD's, backup your system, image your computer. The responsibility is on you. It's like a car, you expect it to work for a while, but without some maintenance, it will breakdown.