Other than technically you might not be licensed to use it, no, it should work. I had that version myself and as I recall, it had to be registered through the distributor but there was no copy protection other than a serial number.
It sound like you’ve fallen foul of Steinberg’s clearly out-sourced call-center support; there are some mods on here who are usually more helpful.
The reason I would urge caution with offers of “upgrades” on auction sites is that Steinberg upgrades are usually just an activation code, like a single-use password, and there’s no way to tell whether it has already been used or not. It would imply that someone had bought an upgrade code back in 2004 or whenever, and then for some reason never used it. I’m not saying these don’t exist, but personally I think it very unlikely.
Once you’ve converted your old projects, and if you haven’t already been completely put off by Steinberg support, you might be interested in the current offer of 40% the upgrade to Cubase Pro 10 from your Cubase Elements 8, valid until August 15th 2019.
Cubase Pro 10 Upgrade from Cubase Elements, LE (4 or higher), AI, Essential, Studio, SX, SL or Sequel
… and no, I don’t get commission – I just think this is really good value. That license would also allow you to run SX3 and all other versions and editions of Cubase.