This was being a single add on to your LATEST post . . .but since . . . IAN has moved here to unitize all prior replies .
Sir Dylan Lie . . . . .
You didn't quite give totally overall encompassing photos, but I can make out that the LED display panel is divided up into two series LED portions.
The yellow is a common ground connection of the two strings and the white and red lines receive power.
Probably the division is because the battery voltage cant supply a TOTAL, single string of LEDS.
If this unit has been unplugged and dormant for a year or so, the probable cause is the time related internal self draining leakage of the rechargeable battery.
This units little configuration of a " trickle " charger that is being derived from the AC line from an isolative capacitor, just does NOT have the OOOMPH required to get that battery back UP to a present charge level state, such that it will then be receptive of a mere trickle charging level.
PROCEDURAL:
Testing done with NO AC power connected.
Take DVM in hand and set up to read DC voltage, initially at its 50 volt range. Then you can drop on down ranges to get the most accurate reading.
Greatest expectation is for that battery to be a 9 Volt rechargeable, but remote chance of an oddball 6 Volt rating.
Expecting its battery technology family to be either ni cad or ni mh.
Initially examine the battery case to see if any of that info is stamped / marked on it.
If not, proceed in stabbing appropriate meter probes into the two terminals o the battery,I say stab since it appears to have quite a pb/sn oxide layer built up on them.
Do we have any voltage ? . . .or even a trace of a voltage ?
If not . . . .original battery . . . . . KAPUTTTTTT !
Time to take a quick gamble now.
Get a conventional 9 volt battery . . . .get one of Mamma Cass's fine grit emory boards and clean the rechargeable batts soldered connections . . to shiny solder . . . but DON 'T break a wire off !.
Set up your units switches / adjustments to the positions that used to make the unit be turned on and be running solely from battery power.
One eye diverges onto the LEDS panel, the second observes the application of the new conventional 9 V battery to the rechargeable batteries cleaned terminals .
BLUE is positive polarity on the RECHARGEABLE battery and you can confirm polarity from its markings on the new battery.
Make a quick battery connection, just long enough to see . . . .if the LEDs come on ?
IF so . . . are they about the same brightness as they always were being before ?
If not, the next confirmation would be to get assistance of another set of hands, to hold previous DC metering to the rechargeable battery, while the new battery is swung into contact again.
IS the OLD battery loading down the new battery, such that its voltage is seriously being pulled down ?
Gonna stand by to wait for your progress . . . . .
Then the REAL magic can start
73 's de Edd