Vintage Synth Repair

Hi, there! 

I have a Korg Wavestation, the first model. The display is not 
lighting, and there is a high humming sound (from the power supply 
area, I think). 

What could be the problem with this? 

The LCD display itself is working, but no light.
Everything else is working fine.

Is this a problem with the power supply or with the display?

Best regards,

Ambrosia