Long and frustrating story. According to Apple Time Machine Restore doesn't work with High Sierra (Yes, that's what I was told over the phone yesterday by Apple tech support). So, I had to use Time Machine Migration Assistant. Unfortunately, this has left Parallels Desktop 100% broken. It will not start (just sends an error report when I try).
So, when I click "solution" (see screen capture) I am brought to a page that DOES NOT include Parallels Desktop 15 (that's what I was running). The highest available form this website is Parallels Desktop 14. This is the page that I'm brought to: https://kb.parallels.com/en/123204 Should I just install Version 14 anyway?
So what's the problem? Did you try to reinstall Parallels Desktop version 15 ? I believe https://kb.parallels.com/en/123204 can be applied to Parallels Desktop version 15 as well.