I would like to add, for the issues you are having with connectivity, they could be related to an IP address conflict.
Lets say you have a service from AT&T. They will provide you with a service drop and 1 usable ip address. They will typically have it set that ip address automatically. That is called DHCP (make sure yours is automatic).
That device will either be your modem or your router. Once you hit a router, it routes multiple IP addresses back on the 1 usable address AT&T provided.
You are correct that with your service on the first floor, you would need to come out of the router, to one of the ethernet outlets in the wall, then plug that into the switch in the basement so that all of the other cat5 cables plugged into the switch can be connected downstream of the router.
If this is device specific, as in your laptop particularly is not connecting to the internet, but your other devices are. Try opening command prompt and typing, "ping 8.8.8.8" and see if you get responses. That is google.com's dns address. If that works, then you are most likely incorrectly configured on the laptop.