With a multimeter, you can essentially reverse-calculate the important specs for the LED. Make a simple circuit (LED, resistor, 5v DC) then test current and voltage drop across the LED. Test for a couple resistor values until you find something you want in terms of brightness and power, then use the voltage drop and current readings you get from that resistor in your chart. If it's a typical 5mm LED you might start at 1k ohm and test a few points down towards 200 or 300 ohm.
I'm pretty new to this whole microcontroller scene and have never used a max7219, but can you post your code? I would imagine that getting the wrong resistor values would just alter brightness, not operation.