You don't need the floppies to upgrade. You don't even need to run the old 1.x version.
Just download the 2.3 demo version, then when you've paid for the upgrade and you get the download permission, make sure you get the V2.3 keyfile, it's not obvious on the download screen. Dump it in the same drawer where you unpacked the demo, the install script will do the rest. It asks for your new 2.3 drawer, and the old 1.x drawer, then drops a new "V1" keyfile in the new drawer. With your new "V2" keyfile, you're on your way.
The old version will still run and is still registered. You can copy your old hotlist across to the new drawer ("IBrowse-hotlist.html").
tony