Depends on exactly what kind of license you have. If your Office disk has a Dell label on the case or envelope, it's an OEM license, meaning it's only legal to use on the computer it came with.  An OEM license dies when the computer dies, which is why it's considerably cheaper than a retail license. A retail version of Office - with a Microsoft-only label and key - can be legally moved from one computer to another. This FAQ from MS gives more detail on OEM license restrictions -  see "Transfer of License".   www.microsoft.com/.../licensing_faq.aspx This may help you as well: www.microsoft.com/.../Default.aspx
I have an old Dell Dimension 4600, with which I purchase a license for MS Office 2003.  That machine no longer works, so I am wondering whether the license allows me to move it to my newer Dell XPS 630i?
Move Office 2003 License to Newer Machine?