New Unmanaged Switch Doesn't Connect to Router

Hi, all. Thanks in advance for any help anyone can offer.

Been running an Linksys BEFSR81 wired router, four port. Got a new laptop
and need to connect. Bought a TP-Link unmanage five-port router. Connected
it by the AC adapter and a new CAT 5e cable going from the laptop to the #1
port of the switch. Supposedly, you don't have to do anything.

Well, ran the setup wizards for both the network and the Internet connection
and although the icon at the bottom popped up and said I was connected, I
cannot connect.

The main computers are all running Windows XP Home, SP2, the laptop Windows
XP Pro, SP3. I did try plugging an existing connected computer out from the
router and plugging it into the switch but it didn't connect either. Then I
took the plug that comes in from the cable outside and tried plugging into
the switch but that didn't give Internet service either. I am stumped.

It may be obvious to someone who knows switches, but I don't and it isn't.
I did use the ipconf/all command on the laptop and the only thing I feel is
worth mentioning is, it gave a line that said NetBOIOS over Tcpip is
disabled, if that means anything.

Thanks for any help you can offer.