Short answer: yes
Long answer:
Although microsoft does not want you to use that on a different computer, they are legally obliged to let you. So what you need to do is the following:
- Download a compatible ISO from microsoft. Compatible means, that you need to use a Windows home ISO if your key is a home license (and vice versa for professional and ultimate). It does not matter if 32 or 64bit, that key is functional on both (but only one installation at a time), so you should obviously get the 64bit iso.
- Either burn it to dvd or make a bootable usb stick.
- After installation, load your windows up with up-to-date drivers and see if it runs fine. Then try to enter your license key. Windows will most likely decline the activation via internet, so use the automated phone activation. Just call the free number provided by microsoft and follow the instructions.