|Is that router even VLAN capable?|
In a typical, multiple VLAN configuration, one interconnects network appliances (ie: routers/switches) using trunking on uplink ports.
Are you using more than one VLAN?
If not, reset your switch to factory defaults and start over. I suspect if you do so, you'll see VLAN 1 is the default VLAN and it will be applied to all ports on the switch. Then all you would need to do is plug a connecting network cable from router to switch and clients attached to the switch should have internet connectivity as well as LAN connectivity.
I don't know why you have VLAN 0 or where that came from but that might be the issue. At least, I've never seen VLAN 0 in use on any switch in any network I've ever worked on.
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.