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First, regarding your backup discs for another, I'm afraid that no, those will not work. Each set up discs are specific for that machine and will not install on another computer.
Now, if you only have a COA for the OS, but no product key, then you'd need to buy the OS with a product key. For Windows 7, since it's no longer sold directly by Microsoft, you'd have to buy it from a third party. One example would be PC Destination (www.pcdestination.com), but you can find several other retailers just by searching for "purchase Windows 7."
If the hardware can handle Windows 10, however, then that's what I would recommend going with. You can purchase it directly from Microsoft via their website at www.microsoft.com/Store/Windows.
Those would be your two options. There is unfortunately no free way to download any version of Windows at this time.
If you have any other questions on this, just let me know and I'll be happy to answer them for you.
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