As long as you removed Windows Vista from your old computer (by reformatting the hard drive), you can then install the same version on a different computer. You may have to "activate by phone" if internet activation is not successful.
You can reset your Windows Vista activation by performing the following:
1. Click on the Start button and in the Start Search box type in: slui.exe 4
2. Press the Enter key on your keyboard.
3. Select your Country.
4. Follow the instructions for phone activation.
5. Once completed, restart your computer.