[Alan Anderson]

Do you see a green "connect" light on the cRIO's Ethernet port, or does it remain dark?

Almost every modern device with an ethernet jack will connect to any other device using either a patch cable or a crossover cable. The cRIO is an exception; it will not switch its transmit and receive pins to accommodate what is at the other end of the cable. If your computer similarly does not automatically switch, either because it's not designed to or because it's been configured not to, then a crossover cable ought to make the connection work.