For sure hook up all 3 wires Rx, Tx, Gnd. This is a signal ground and should not be a problem. Generally, shields on long cables should not be connected at both ends but the signal ground needs to be there for serial communications.
Always try swapping the Tx and Rx lines. Even if you are sure you are wired exactly as the documentation says, you have to remember that one side's Tx is the other side's Rx. If the person who wrote the documentation was looking at it from the other side you were, then you'll have it reversed.
Before wrestling with the SLC, see if you can get the display working from your computer with Hyper Terminal or some other terminal emulation software. This will allow you to play with port settings much more easily than through the PLC. Once you can type the characters on your screen in Hyper Terminal and see them come up on the display, you'll be able to use the same port settings in the SLC and know they are right.