I'm not at all familiar with Solus, but I have seen something similar with Manjaro.
Some releases will refuse to install from a DVD, no matter what you use to write it, while others will refuse to install from a USB and you end up having to use a DVD...
I will say it doesn't sound like you have any problems with your DVD drive, just that one DVD itself, which, yes, it might be useless now. If you are getting it to read in one version of Linux, I'd try blanking it in that version or distro... that might allow you to rescue that disc for later use.
If you're dead set on trying Solus, maybe try installing from a USB instead?