Media for Putting a switch between router and cable modem

Putting a switch between router and cable modem

Hello, Here is my current config (downstairs in my basement) :

Coax cable into cable modem (this is the only cable access I have in my house) Ethernet cable from cable modem into Linksys 4 port wireless router WAN port

2 computers plugged into ethernet ports on the router (1 from a long cable run from upstairs) Wireless access for 1 laptop

The wireless access is poor upstairs in my house. I'd like to move the wireless router upstairs. I have done this, connecting the the ethernet cable with the long cable run from the WAN port on the router directly to the cable modem downstairs. The problem is I now don't have the router downstairs to plug my downstairs computer directly into.

Can I put a switch between the cable modem and the router? I tried it with a hub I had laying around, and it didn't work. Would a switch do the job?