OEM disks supplied with computers will, in general, only work on that system. In any case, even if you could install on another computer you wouldn't be able to activate that copy of Windows a second time. I appreciate that you want to save money, but if the insurance paid back the cost of the computer that did include the OS (as you say, it was part of the original computer), so you're not really out of pocket.
The best you can do now is to buy a generic OEM version of Windows 7 that is not tied to any computer. But that will have te same proviso that you would never be able to use it on another computer in the future.
If you really want to save money you could always investigate Linux; great if you just want to do web browsing, word processing, programming, etc. but not so good if you want to play games.