Vintage Synth Repair

I got this one a few days ago, very nice cosmetic conditions. Here's 
what I got -

1. The synth plays no sound at all, an non of the voice cards' LEDs 
light when playing. When I play the keys, all I can hear is low 
static noise at different frequencies (the more keys I hit at once, 
the lower frequency the static noise sounds...)

2. The voice card at the 7th position is missing, I set the DIP so 
7th miniswitch is turned downwards (towards the text saying "OPEN") 
and all others upward.

3. Battery was dead, replaced with a 3.6v NiMH battery.

4. When I press the various buttons, I can see that it responses as 
expected - i.e. I can switch between presets, switch modes on/off. 
etc... many switched do not respond though, but I guess that many of 
them have contact problems...

5. There's a component which is soldered directly between two legs of 
the big transistor mounted to the back of the synth, the left-most 
one. That component is totally fried out...

6. The synth has been stored for many years.

First mission is making it sound... i.e at least I'd like to see the 
LEDs on the voice cards light up when playing... I understand that in 
any case the OBXa has some value out of the tolerance specs, it won't 
play at all ?? is that right ? but would the LEDs still light ?

I'd be more than thankful for any help or directions....

Thanks !!!