Removing it from your old pc and installing on new shouldn't present any problems,there is still a 120 day period for hardware changes where telephone activaton is needed.
Extract from the licience agreement from windows 7 (rtm) biuld 7600-16385-090713-1255.
this is the release version that will ship in October 22.
1. OVERVIEW.
a. Software. The software includes desktop operating system software. This software does not include Windows Live services. Windows Live is a service available from Microsoft under a separate agreement.
b. License Model. Subject to Section 2 (b) below, the software is licensed on a per copy per computer basis. A computer is a physical hardware system with an internal storage device capable of running the software. A hardware partition or blade is considered to be a separate computer.
2. INSTALLATION AND USE RIGHTS.
a. One Copy per Computer. Except as allowed in Section 2 (b) below, you may install one copy of the software on one computer. That computer is the “licensed computer.”
b. Family Pack. If you are a “Qualified Family Pack User”, you may install one copy of the software marked as “Family Pack” on three computers in your household for use by people who reside there. Those computers are the “licensed computers” and are subject to these license terms. If you do not know whether you are a Qualified Family Pack User, visit go.microsoft.com****************** or contact the Microsoft affiliate serving your country.
c. Licensed Computer. You may use the software on up to two processors on the licensed computer at one time. Unless otherwise provided in these license terms, you may not use the software on any other computer.
d. Number of Users. Unless otherwise provided in these license terms, only one user may use the software at a time.
e. Alternative Versions. The software may include more than one version, such as 32-bit and 64-bit. You may install and use only one version at one time.