You have 3 online activations every 3 months. If you attempt to activate more often than that, you need to call Microsoft. If you plan on removing the old install and installing on the new computer, you will have zero problems. Unless you install and activate Windows more than 3 times in the 120 days. Then you'll have to call. And you still will have no problems. So long as you arent trying to do anything illegal. Just install Windows on your new computer, you'll be fine.
\Dan