Is your miner setup for DHCP?
Why I ask:
Several cable providers offer up to 10 IP addresses that will DHCP through the modem. If Time Warner doesn't (they are known for their stingy behavior) then you'll need a router.
If so, you can pick up a very cheap (under $10.00) router or switch from Ebay. The chances of them being bad are very slim. All you need is a simple 4 port router and you're good to go.
Let us know how it goes

-H