Hello and thank you for choosing just answer.
If you don't have the copy of Windows that came with THAT computer, whether its the recovery CDs or drive, then you would have to purchase windows.
You cant use discs for other computers, doesn't work that way unfortunately. But you are allowed to re-insall.
You should CALL Microsoft, and explain to them, they will issue you a new product key.
1. Press Windows key + X then clickRun, then type: slui.exe 4
2. Next press the 'ENTER' key
3. Select your 'Country' from the list.
4. Choose the 'Phone Activation' option.
5. Stay on the phone (do not select/press any options) and wait for a person to help you with activation.
6. Explain your problem clearly to the support person.