Well, the max light from a LED is determined by its Ampere value, and to reach that limit you have to know its Voltage requirements.
So, if your LED only shines with, say, 5mA you wont get it to shine very brightly no matter how much juice you add (unless you add too much and it gets extremely light for a nanosecond, goes pop and then it smells like hell the rest of the day. lol).
Take the ones I use for example: their \"statline\" is 3V and 20mA. Which basically means that when they are fed 3 Volts they shine with 20mA.
So, assuming your button cells are 1,5V each as the most common ones are, that would mean that you would get 4,5V out of them and therefore make LED\'s of the size I am using pop(or in a best case scenario, only shine a very short time) if I wouldn\'t have a resistor in the circuit or if the diodes used demands say 6V you wouldn\'t get them to shine bright at all.
When testing my contraptions I use a homemade battery pack made from two AAA batteries taped together so that I get the nominal 3V for my LED\'s and they light up fully.
But(![!!]), connecting them directly to a power source fatally reduces the life length of a diode, making them last a very short time compared to what they should( and would), you should always add a resistor to the circuit!
what resistance your diodes need is calculated this way:
R=U/I Resistance=Voltage/Current
Voltage is calculated easily by taking the amount of Volt from the battery and subtract the amount used by the diodes. My Situation:
I use a 9V battery in my tank and my diodes crave 3V each, using one diode I get 9-3 which sums it up to 6V left in the circuit.
R=6/I
The Current is the Ampere the Diode uses. In my example:
my diodes have 20mA, 20 milliampere, which converted is 0.020 Ampere.
R=6/0.02
And this means that the optimal resistance for my circuit is 300 Ohm.
But even if you use the exact amount of volt the diode demands you would still need to add a resistor even if you get 0.0 in the calculations, this to prevent the diode taking damage to power fluctuations which constantly occur. And as long as the resistor isn\'t so strong that it totally blocks the entire current you basically get the LED to light up at full strength since it doesn\'t light up in a linear fashion like a light bulb does(Warning: technical overdose here, let\'s just leave it at that and be happy. lol It still works).
I feel I started off on a minor rant here, I hope I made some sense and that it gave you some kind of answer to why you wont get your LED\'s to light up as strong as you want even though I didn\'t actually give you a direct answer at all. As you can see there are a few factors that might be the problem.
Oh, and another thing, this is probably rater redundant to mention but still, if you connect a diode backwards it wont do anything at all, Anode to + and cathode to -, that\'s the only way to go.
I am off to work now so see you later guys!