I had exactly the same problem today, and I was lucky enough to solve it.
Here's what helped me:
With Suspicious Package installed, I was able to identify the script in StarTech's installer pkg. It' called "postflight".
Amongst other things, postflight runs this command:
sudo mv usr/share/sandbox/mDNSResponder.sb usr/share/sandbox/_mDNSResponder.sb
A quick check in Apple's knowledge base revealed, that the mDNSResponder is essential to use DNS (i.e. to resolve server names like www.apple.com) and bonjour.
I moved th mDNSResponder back to where it belongs:
sudo mv usr/share/sandbox/_mDNSResponder.sb usr/share/sandbox/mDNSResponder.sb
After a reboot, everything worked fine again.
I have no idea, why StarTeck disables an essential tool. Let's assume it's an error ...
But after this experience, I didn't want the StarTech ethernet driver on my machine (I had installed it just for curiosity, anyway - yes, I know, I shouldn't have ...), so I removed the kext the installer had copied to my system:
sudo mv /System/Library/Extensions/IONetworkingFamily.kext/Contents/PlugIns/AppleIntel8 2580.kext /Users/myusername
(You see I didn't delete the kext directly, I just moved it away and tried another reboot. Now everything works fine, so I'm going to delete the kext entirely and paint a big red cross on StarTech's installer disk.
Hope this helps.