AHA, a clue. I should have mentioned that I was not familiar with the ER-16. From what you have described, I would bet that the DIO port is configured for input (read) instead of output (write). This will cause a high impedence closed circuit. There is a pull up resistor on the input of the DIO when configured for input (reading). The current goes through the pull up resistor and into the LED circuit, causing a dimly lit LED. I am quite sure that the port is configured for input. Change your code to configure all the ports at the beginning of the block diagram before anything else happens. Use a sequence structure if you have to in order to ensure that this config happens before anything else. Then do not use the DIO config vi again. This should clear your problem. By having the config vi all over the place, it is possible that the other DIO channels gets configured to a default state of input when you are actually configuring channel 0 for output. Look up examples on DIO config and use the help feature to find out the best way to configure multiple channels of the DIO for different directions.
If all are output, I think you can make an array of all the channels and use only one config vi to configure all for output at one time. Use the function DIO Config.vi found in the functions palette at NI Measurements - Data Aquisition - Digital I/O - DIO Config.vi. This will do all channels at once. Just wire an array containing all channel strings (a string array with elements of 0,1,2,3) to the Port List input of the config vi. Wire a numeric 0 for the group number. Right click on the Group Direction input and create a constant. It will create an enum in which you can choose "output". Wire in the device number. No other inputs are needed, leave them unwired. Use the DIO Write function from the same palette, pay attention to the write location input cluster to choose which lines to write to.
If you do not want to group all ports together, just config one channel at a time and be sure to use the task id output from config to go to the correct group write input.