Yeah, the TL-SG1016DE is plug and play if don't need the advanced feature. I don't konw how do you connect the devices. Generally it's Internet<---->Router<---->Switch<---->PC.
Check the PC whether can an IP address from Router, and whether the Router can access internet.

If you want true plug and play, you need a TL-SG1016 (without the DE on the end). TL-SG1016 is a simple network switch that is true plug-and-play. The TL-SG1016DE is a managed "smart switch" that is most often used in a small business environment where you need segregated virtual networks (VLANs).

Also note that VLANs and plug-and-play are not compatible terms. All VLAN environments require network planning, design, and most importantly, active administration.