Describe your VLAN configuration on SG108E in details.

[/TD] [TD]vlan1	vlan10	vlan20
member ports	1-8	1-5	1,6-8
tagged ports	[/TD] [TD]1	1
untagged ports	1-8	2-5	6-8

This is all I have setup now. What else to I need to change?

Thanks!

Would this be an issue with my router? Do I need to set my router to route traffic through to the switch somehow?

So your setup is:
Modem/ internet --> old cisco (in WAN port) --> old cisco (port 1, 2, 3, or 4) --> GS108?

Does your router support vlan?
Since you seem to be tagging the traffic from the switch to the router.

If so, I think you'll need to log into the router, and also setup the vlan settings in there. So the router knows what the vlan tags mean, and what can and can't do.
I suggest you start without VLANS, if it works...
Then 1 VLAN. try to set it up on both router & switch.
once that works, add the second VLAN .

This router does not support Vlans. Does that mean that I need to untag port 1? Thanks.

Don't think you "have" to. The tags will use be ignored by the router if he can't read it. But then again.... if it won't be used you might as well disable it.

I would try this setup:
VLAN 10(group1): port 2 - 4 + port 1 // all untagged// set PVID to 10
VLAN 20(group2): port 5 - 8 + port 1 // all untagged // set PVID to 20
VLAN 22 ( router ): port 1 /// untagged /// set PVID to 22

connect port 1 to your router LAN port
connect Router WAN to your internet modem,

try Internet from group 1 and group 2
If no Internet, I would try connecting port 1 to the up link port.

You can also try pinging the modem or a site from group 1 and group 2
And ping a computer in group 2 from inside group1 (and visa versa... To check They are seperated)