Cisco Switching/Routing :: Router 101 For Dummies?

I am a service provider, with the task of installing a systech device at a site, and was told all I needed was DHCP enabled and dynamic IP for the internet.  The site just put in broadband and their router has a single port.  I picked up a linksys dsl router to use as a router/switch to enable more ports for the internet.  If I hook the broadband router into the internet port of the linksys, I can not get internet access on my laptop through it.  If I hook the broadband to port 1 and my laptop to port 2, I have internet access.  If I hook the systech device to port 3, the support team says they cannot see the device.  But, if I hook the broadband directly to the systech box, they can find the mac address and download to it.  I have set the linksys to default settings, but will not work.