Static IP makes network unusable.

Honestly this has nothing to do with DietPi. DietPi is always sending the DNS request out but somehow it did not get an answer back if you use a global upstream DNS provider. This we already tested using tcpdump Probably this is blocked somewhere. But for sure it’s not something in DietPi or the base image below. At least as long as you don’t install any tcp blocking software. DietPi did not know if you use a local DNS server like your router or a global public DNS server. Simply the configured DNS server is used. To find out what is blocked and where, you would need to continue tracing inside your local network and try to capture DNS packages. Maybe your router is offering such possibilities. As well you could use Wireshark on the computer hosting the VM to see what is going on.