Controlling a Giant LED Dot Matrix Sign through RS-485

pylon:
This looks like a signal from a floating bus. Is that bus in a defined state (using pull-up/-down resistors for A and B)? The number of resistors on that RS-485 converter would lead to assume it should have these in place. Do you have schematics for that board?

According to your wiring description RO is not connected. Please post a wiring diagram (may be hand drawn) of your setup.

Initially RO was not connected. I connected it to RX1 to answer the question of am I receiving data

I do have resistors on the line, as shown in the documentation below, I tried using 4.7K resistors like they show but I stopped receiving data completely when I did that, so I went with 10K, and skipped the capacitors.

I found some really odd documentation that suggests that I invert Arduino's TX line with a NOT gate and connect that to DE, then connect Arduino's TX1 line to RE and DI, then connect Arduino's RX1 to RO. I tried this but it didn't seem to change anything.

UPDATE:
Just noticed that one of the IC's on the RS485 converter has a suspicious "bubble" coming out of the top of it. I'm assuming I blew it up in my last project that I never got working. I tested this by turning the baud rate down to "1" and placing an LED on each side of the converter, the led on the Arduino side flashes many times but the output only flashes once. I ordered a new converter.