Having problems with a window comparator
The LM339, like many comparators, have open-collector outputs which can only pull to the negative supply. They can only sink, but cannot source, current.  This means that the solution to your problem is easy: just tie the two comparator outputs together. Then either comparator can pull the combined output low.  You can use this output to drive an LED directly, but you will need a series resistor, as mentioned in the comment above.  Likewise, connect the supply pin directly to the battery.