Diagnostics time 
I was expecting to find some dry solder joins ( I've see other folk say this was the problem with their lights, and we all know LEDs last forever ... right ?)
You can use a 9 volt PP3 battery to test the circuit on the bench (connect the blue wire to battery postive)
Connect the battery then either :
Option A - look around each LED, if you see any dry solder joints - resolder them and hope it's fixed (all of my problems were due to dead LEDs not dry joints).
Option B - use a multimeter to measure each LED, check the voltage across the pins of the 1st LED, then across the pins of the 2nd LED etc ... working LEDs give voltages under 3 volt, faulty LEDs show over 6 volts.
Option C - use a small screwdriver, short the pins of each LED in turn until the unit lights up.
Note. LEDs must be connected the right way around, if you connect them "backwards" nothing will work (think of them as a 1-way valve for electricity)
You should then know which LED is faulty.
You can hold a new LED in place across the faulty LED to check things work, then make a note so you fit the new LED the right way around.
replace the faulty LED first - retest and you should now have 3 working LEDs
Optional - replace the other LEDs so you have a matched set.