Processes in Microsoft 365 for setting up Office apps, redeeming product keys, and activating licenses.
Don't waste your time -- even if Office 2004 were available for download it cannot be installed on OS X 10.7 or later. Apple withdrew support for PowerPC software & discontinued the required Rosetta emulator that enabled it to run on Intel Macs.
What you've been finding are updates to Office 2004, not upgrades. Updates are "tune ups" that improve compatibility/performance/etc. of a specific version. They require that the base installation of the version to which they pertain be installed. IOW, you cannot apply an Office 2004 update if Office 2004 isn't installed.
Having upgraded your OS you need to upgrade your software accordingly. An upgrade is a newer version/release of the actual software. Office 2011 is the most recent release of Mac Office & will operate on any current version of OS X, 10.5.8 or later.