> The headphone jack is quite noisy and when I do
> a number of functions, there is this sound
> that comes out. ...

Everything is relative - but the headphone output does generally have some
'digital' background noise. I seem to recall that there was a HW mod on
most/all Polarii to help improve on this (i.e., a separate ground wire run
to the little board near the output jacks). Even with that, it doesn't
completely go away.

All things being equal, the noise should be considerably lower than any
sounds actually made by the synth itself (i.e., easy to hear if there's no
output - but once you start to play, it should pretty much be swamped by the
intended output).

> ...The output jacks do not work at all which I know
> is not normal...

A few ideas ...

If the keyboard looses it 'calibration data' (for instance, if the internal
batteries are totally dead - which to be honest, I've never seen in a
Polaris - or if the panel sequence is executed to do a 'computer reset'),
then you won't get any meaningful sound out of it until the calbration
procedure is executated again.

Another (less likely) possibility is that 'local control' is turned off on
the machine - so that it is only going to generate local sounds if they're
sent to the keyboard via MIDI (vs. responding to keystrikes, etc.)