This post is running very close to a line that CH members cannot cross. Which is advocating or promoting any activities which are illegal.Therefore "it has an "illegal" version of windows 7 on it,
she doesn't want to buy a new OS, is not a subject we can address. This statement MAY provide some solution "the vista product key is still readable underneath,". You can try contacting Microsoft and telling them that the original installed version of Vista no longer functions and that you do not have the O/S disc (very common to be so) nor do you have any recovery discs. By supplying the product key you may be able to have them provide you with disc for the O/S (it won't be free--but it will be nominal as opposed to buying the software retail).
"is it acceptable & moral to copy another (my) vista OS + use her original product key?" Generally speaking an O/S supplied with a computer (discs) in this case yours are specific to a particular computer(yours in this case) and while you MAY be able to install it when it goes to touchy feely with Microsoft --which it will do at some point you may lose the use of the computer it is installed on (hers). No matter which way you go you may encounter problems which will necessitate the purchase of a legitimate Windows O/S.
There is however an alternative to this and that is install a free version of Ubuntu or there is another company that also has a free O/S available (it escapes me as to who it is). Others may know the name. I think Chrome also has one. truenorth