There is a 99% chance it will activate over the Internet without a problem.
If it doesn't, it will give you a phone number to call Microsoft (in your locale), and you can explain what happened and they will help you activate it.
Here's a blurb on changing hardware and activation, from Microsoft's site under "Myths About Activation":
Product Activation keeps users from changing or upgrading their hardware.
Not true at all. Users can change or upgrade their hardware. One of the forms of piracy that Product Activation guards against is hard disk imaging. Not all forms of hard disk imaging are illegal. In the case where a pirate copies data from one PC hard drive to another to illegally run the software on two PCs, Product Activation stops that by forcing the copied software to be reactivated. It does so by comparing the hardware on which it was activated to the hardware on which it is now being booted. If the hardware is substantially different, then reactivation is required. If it is the same or similar, then the software will continue to work. Those who upgrade their PC's hardware substantially may be asked to reactivate. Reactivation for this reason is easy and can be completed by contacting Microsoft to obtain another confirmation ID.