This problem happens quite frequently. Unfortunately you need that disk.
That screen where you click "I Agree" says:
UPGRADES. To use Software identified as an upgrade, you must first be
licensed for the software identified by Microsoft as eligible for the
upgrade. After installing the upgrade, you may no longer use the original
software that formed the basis for your upgrade eligibility, except as part
of the upgraded software.
and
SOFTWARE TRANSFER. Internal. You may transfer your copy of the Software to
a different device. After the transfer, you must completely remove the
Software from the former device. Transfer to Third Party. If you are the
person who initially licensed the Software, you may make a one-time
permanent transfer of this EULA, Software and Certificate of Authenticity
(if applicable) to another end user, provided that you do not retain any
copies of the Software. This transfer must include all of the Software
(including all component parts, the media and printed materials, any
upgrades, this EULA, and, if applicable, the Certificate of Authenticity).
The transfer may not be an indirect transfer, such as a consignment. Prior
to the transfer, the end user receiving the Software must agree to all the
EULA terms.
What it all boils down to is if you don't have the software, you can't use
it.