Not without the install media, it isn't possible. However, you could use something like MagicJellyBean to recover the license key and then borrow an Office 2003 disc from a friend, and reinstall, using your key. Keep in mind, this technically isn't legal, as the person who sold you the computer should have included the COA with it, and you should have asked for it as well.
If that doesn't work, or isn't an option, don't both with an installed version of Office, and just use Office Live.