All you can do is try. Each Windows disk product ID is coded. There are 25 digits. One digit refers to the CD, another to the version. And some refer to other codes in the chain. Some of the code determines machine. Some determines model. of those refers to another one to determine machine, etc.
Then restore disks are different still.
A few people have cracked the code on some machines... but they used master computers to do it.... even the code changes by the pattern and digits of the product ID. When you do the math, the possibilities are mathmatically enormous.
Some manufacturers are careless or corrupt, and did not post the codes they way required by Microsoft... perhaps to save money they have to pay Microsoft for each install code.
This is further complicated by the EEPROM chip which was once 6 digits, then 7, and now 9 or 12... If the disk does not detect the correct EEPROM code, it cannot install.
Bottom line, if you do not have the correct disk for the machine, you don't have a prayer...
But you can talk to Microsoft. Their Canadian office helps resolves legitimate claims... and allows you to buy replacement disks for a small fee. I have not purchased any recently, but have in the past obtained them for under $50... for a specific machine or a specific product ID... You have to be convincing, and they have enough information to know you are blowing smoke if you try to create a justification.