Ethernet/Network

I just recently got a 1gbit router, however I am having problems with it. I hooked it up to my cable box and then to a switch. The switch then has 8 ports that flows to various computer/printers. The internet is not working with wired, but only wireless... Right now I tihnk the problem is because my switch/hub is a 100mbit. Is that true? I also have a cat6 cable and can link that directly from the router to my computer which works.
Also I have another computer that has a 100mbit network adapter on the graphic card... that computer doesnt work.
Do I need everything to be 1gbit?

 

How about you start with some basic info? The make/model of ALL the equipment is a start. You do NOT need gigabit all around, I have a mix of gigabit and 10/100 equipment and switches here, everything works fine.

Please detail exactly how you're connecting everything too.