If you bought the OEM version, it is tied to one computer, so legally it cannot be installed on another computer. If you have the full version, as long as you only have it installed on one computer, you can transfer it to your new computer. The "upgrade" version is more similar to the full version than the OEM in this regard.
Even with the OEM, you can probably call MS and get them to activate, just as long as it is only on one computer. The longer period between activation, the more likely it can be done over the internet very easily. I had a full version of XP Pro that was in like ten different computers, although only one at a time in sequence as I upgraded. Nine out of these ten times it activated just fine over the Internet. The other time, when there was only ten days between activation, because of hardware problems, I was required to call. But I didn't have to talk with someone, just entered some keys that the computer voice told me to and away I went.