Hi, I'm from Tahiti (french Polynesia) and I'm surching a mother board or main board for my keyboard (Korg I3)

You will need to open up the keyboard. Make sure it is unplugged. Once you take out all the screws that hold the top half with the bottom, separate the two carefully. You will have some wires and ribbons attached to both sides. The battery is on the circuit board, it looks like a quarter. Make sure you replace the same size battery.

If it's just the backlight, and you're good with a soldering iron, here's a link to the supplier I use. http://www.telesisgear.com/id16.html
This Youtube video will give you an idea of what's involved even though it's for a different instrument
Korg Wavestation Replacing Backlight by Davide Solurghi Morpheus2027

The details are highly confidential and have only ever been released to engineers under Non Disclosure Agreements, who work closely with Korg in the design process. If anyone tries to tell people about it on the forum then a breach of an NDA has occurred and whoever did it could be sued by Korg. The person posting those details could have their account on the forum suspended.

Please understand that there are very good reasons why Korg want to keep those details confidential. The functions were designed for use in the factory when the keyboards are manufactured. Two of the functions can completely wipe the internal SSD and the boot EPROM rendering the complete keyboard unusable. One of the circuit boards would have to be returned to a factory for the chips to be re-initialized using specialist hardware plugged directly into the CPU board. The necessary hardware to re-initialize the SSD and Boot EPROM is not even available to Korg service centers.

If you are someone who has discovered the way to access the system diagnostic menus, then there is a high risk you will completely trash your Pa2x/ Pa800 etc, turning it into a "brick" that will no longer be capable of reloading the OS or factory data. Korg representatives have said to us several times that damage caused in this way is NOT covered by warranty. If two of the functions in the system diagnostics menus are used, then to get the keyboard working again, service centers will have to replace the complete "main board". This is the board which contains the SSD and boot ROM chips. You are looking at a repair cost of over $800 plus shipping.

Initialization: Hold Edit/Style and Arrange/Play while turning it on.
Preload: Disk Load (IFD01P for i3 and i2, IFD02P for i1)
ROM Check: Hold Enter and 7 while turning it on.

Step 1:
Check the setting of LOCAL CONTROL in GLOBAL mode.
Go to GLOBAL mode page 1 (Figure 1-2):

Move the cursor from the MASTER TUNE to LOCAL CONTROL. Setting LocalControl should be in the ON position.
When the setting is OFF,set it to ON (use dial TEMPO / VALUE or DOWN / UP button).
Go back to ARR or PROG mode,and play the key to check audio.

Step 2:
If in step 1, the sound still does not exist, then it is a hardware problems, and the possibilities are :
Figure 3, the section in red shading is a block may be damaged.

Figure 4 is a scheme. Parts that might be damaged in case of no-audio are:
IC 2,4,5 (4570), IC9 (78L05), IC6 (PCM69AU), IC 3 (5216).
Check also the transistors Q1-Q7 (This is the MUTE transistor, and this is most often the cause in case of no-audio).
If you can not fix it by yourself, then leave it to the experts.
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Check the output socket for corrosion, this would stop the sound from getting to the amp. Plug in an output cable and wiggle it around to see if it works intermittently. Plug it in and out a few times and see. We are looking for a dirty connection.

Yamaha YDP223 :

YAMAHA YDP 223 223C PARTS Service Manual free download schematics eeprom...

Korg i3 :

KORG I2 I3 SM Service Manual free download schematics eeprom repair info...

Have you tried it with batteries? Are you sure the power supply is working correctly? It should not need the OS to operate as a keyboard disconnected from the computer.

The cable connection is just a MIDI cable that uses opto-isolators so the 2 items are electrically isolated from each other. The software driver for the Korg should load without problem. The Korg program itself may be looking for inputs that are not there when the keyboard is off and the program itself reaches a stop command.

If the PA80 will not work on just the power supply- the power supply can be the fault- it has an internal fuse. Finding a similar supply with the same coaxial plug wired the same polarity is the way to test it if the battery option is not available.

http://lmgtfy.com/?q=korg+i3+manual+pdf

if your keyboard has been affected by a lightning strike then every semicondutor ( diode transistor i/c ) will be blown ...I know most components are on the mother board but not all ...I reckon cheaper to buy a new one ...sorry