Are you sure the Product Key is valid? Are you sure that there is not another Office version installed in your system?
If you've successfully installed Office 2003 using the same Product Key on a previous Windows version, you could try running the installation program in compatibility mode for a previous Windows version.
If the installation works fine, do not forget to download and install Office 2003 Service Pack 3 (http://www.microsoft.com/download/en/details.aspx?id=8) to achieve full Windows 7 compatibility.
I also suggest you to ask this question in the Office Answers Forum at the following address
http://answers.microsoft.com/en-us/office/forum/office_2003
Bye.
Luigi Bruno - Microsoft Community Contributor 2011 Award