Microsoft Office 2007 on Desktop and Laptop

I just recently bought a new desktop and new laptop from dell and my MS Office Small Business edition came installed on my desktop. I installed it on my laptop and works OK but will not activate because I already activated it with my desktop.

I was reading the license that came with office and I am under the understanding it can be installed on both without the purchase of additional licenses:

"AS DESCRIBED BELOW, USING THE SOFTWARE ALSO OPERATES AS YOUR CONSENT TO THE TRANSMISSION OF CERTAIN COMPUTER INFORMATION DURING ACTIVATION, VALIDATION AND FOR INTERNET-BASED SERVICES.
IF YOU COMPLY WITH THESE LICENSE TERMS, YOU HAVE THE RIGHTS BELOW FOR EACH LICENSE YOU ACQUIRE.
1.  OVERVIEW.  These license terms permit installation and use of one copy of the software on one device, along with other rights, all as described below.
2.  INSTALLATION AND USE RIGHTS.  Before you use the software under a license, you must assign that license to one device.  That device is the “licensed device.”  A hardware partition or blade is considered to be a separate device. 
a. Licensed Device.  You may install and use one copy of the software on the licensed device.
b. Portable Device.  You may install another copy on a portable device for use by the single primary user of the licensed device.
c. Separation of Components.  The components of the software are licensed as a single unit.  You may not separate the components and install them on different devices."

Am I understanding this wrong? Thanks for any help!