My motherboard died on my Vista 32bit PC. The rest of the components are working perfectly. I do not have a recovery disk. Can I use product key on the case to activate a new Vista install?
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I am sorry, but a new Motherboard is considered a new computer. You can use the same DVD, if you had one, but you will have to purchase a new key. I do not think that you can easily buy a key for Vista at this point. If your computer can handle the requirements you may want to investigate buying Windows 10. I have used Vista, Seven and find 10 the be the best (in my opinion).
If you do decide to go with 10 feel free to visit our 10forums. Windows 10 News - Windows 10 Forums
As a member of that Forum, I can assure you that you will receive excellent help with all of your questions.