broken link removed
Your schematic shows 6V battery and 4 LEDs, with Rb=560 C=47uF and a D883 NPN Power with 2 diodes and a battery charger.
Missing is the connection from Vbat- to Vcharge-.
THe photo shows 4VLED on some FPC strip and appears to be all in parallel.
THe D883 specs are:
Collector-emitter saturation voltage V CE (sat) I C =2A, I B = 0.2A 0.5 V
Base-emitter saturation voltage V BE (sat) I C =2A, I B = 0.2A 1.5 V
This means to get 0.5V across Vce, you an need IC/IB= 10 i.e. the base current is 10% of the load.
When charging and the transistor disabled by shorting the lower diode to Vbat-, the current depends on the supply and battery ESR and voltage difference. THe capacitor current is limited by the base Resistor and voltage difference , hence 6V/560Ohm=10 mA
THis means the transistor can only drive 100 to 200mA total and the transistor Vce will rise to the difference between Vbat and Vled, which appears to be 2V.
I would expect each of these LED's can handle this amount 100~200mA. How many to do you have running> and what is your total current?