The voltage is 12v on the brick but because of the battery pack, as you mentioned it looks like DC. the LED panel is definitely custom and requires disassembly to see what components are actually inline. Might be easier to just solder back the battery pack and call it a day.Are those LED's even rated for 120V? Your "power pack" (known as a "Driver") was most likely to reduce or change the voltage from 120 to 12v or 24v... AC to DC (most likely). Since you had batteries inline,I would imagine it's converting to DC. AC would flicker because it's alternating current @ 60 cycles per second...whereas DC doesn't fluctuate...amongst a couple other factors.
You to examine the lamps for their rating,as well as the transformer / driver. an LED is a "Light Emitting Diode" unlike most 120v lighting applications...a filament or a gas.
That's my guess from what lil info I/we have.