rather than split a connection, you can certainly do that as long as your PC is set to get its IP address via DHCP. You will lose some security in doing this as a router is a hardware firewall. With a router, snoopers see it's address. Without the firewall, your PC becomes more of a target for prying eyes.
Would this work? Using a network splitter, I want to split the connection from my cable modem sending a direct connection to my desktop computer (which is NOT wireless) and a Linksys Wireless Router which I use with my laptop.
REASON: Lately the Linksys Router has been dropping connections randomly...when it does this the power temporarily goes off, then the router reboots itself. Since my desktop computer gets it's Internet connection from the Linksys Router, my desktop system becomes inoperable until the router get back up and running. With the mentioned setup, at least when the router goes down, I will still have a direct, unaffected connection to my desktop computer.