It appears that someone has already tried to make some "improvements" over the original three AA cell arrangement. The battery compartment is trashed, spring contacts corroded, some terminals missing, wires disconnected, etc. Did you retrieve this sign from a landfill, or perform the modifications yourself?
All of the LEDs appear to be wired in parallel, which is NOT a good way to operate LEDs. If you want good life from this sign, you should check each LED for brightness and functionality by first disconnecting the parallel wiring arrangement. Connect each LED in turn to a voltage source with a series current-limiting resistor. Replace any LED that fails to light up brightly with 20 milliamperes of current. Ask here if the selection of a voltage source (for testing) and a resistor (for current limiting) is beyond your current level of competence.
Next, connect a pair of small-gauge wires (like the black zip-cord wire shown in your photo) to each LED, with sufficient length to allow all the wire-pairs to be brought back to a common location inside the back of the sign. There you will install a small prototyping board with a current-limiting resistor for each LED.
At this time you may consider getting creative with your sign, instead of just connecting all those wires attached to the prototyping board to a power source. Perhaps a "chaser" effect where the LEDs illuminate in sequence, chasing each other around the sign, would be an appropriate effect. Or perhaps a simple ON-OFF-BLINK-ON-OFF sequence would be attractive. Lots of possibilities now that you have access to all the LEDs independently. Folks here at EP can help with the design if need be.
i have seen a LOT of these cheap "artisan" thingys for sale (mostly in arts and crafts shops) lately. They all look cheaply made on the outside, but worse on the inside if anything electrical is involved. And they are invariably overpriced. However, a well-made sign like yours appears to be, does not have to suffer from inadequate electrical wiring, or limited battery operating life. Spend a few bux to get it wired up properly.