Can you connect to the router on the HP using the same Cat-5 cable you attempted to use on the Toshiba? The reason I'm asking is to ensure the Cat-5 cable works properly and we're not introducing a red herring into the equation.
Click on Start, Run, type in CMD.EXE and then hit the Enter key. Within the Command Line Interface (CLI), type in PING 127.0.0.1 and then hit the Enter key. This is what's known as a loopback address, and is useful for checking to see the TCP/IP stack is corrupt. If you cannot ping it properly, have a look at this Microsoft page for instructions on how to reset TCP/IP, and then try again.
"An ounce of prevention is worth a pound of cure" ~ Ben Franklin