I had same issue where only few blue led blinking happends after pressing power button.
SOLUTION:
(1) Clean any battery leakage contamination in battery compartment terminals using Alcohol (Isopropyl) OR bit of WD 40/ normal after shave lotion.
(2) Insert brand new batteries if testing after long time.
(3) Insert Wii FIT Plus game into the Wii console.
(4) Select your Wii character profile and select body test, it will ask you to POWER ON the board.
(5) Now SYNC the board with Wii console, like your remote. (open battery lid, you will see SYNC soft button)
(6) After successful syncing, the board will be turned ON automatically (BLUE light ON). OR press Power button now and it will light off after few blinks and press again, it will now work normally.