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And some positive news again: For some reason my general Windows network settings also started to have problems, so I ran the standard Windows...
Thanks for looking into it. The report number is 19509734.
Well, don't get excited too soon. For me the problem just re-appeared! :( So if anyone has any other pointers to offer, let me know.
One more thing: After re-installing Parallels, I reset the network settings. This can be done in: File > Preferences > Network > Select an...
Had the same problem, and reinstalling the Tools (both on host and guest OS) did not do it for me. But reinstalling the whole Parallels...