It doesn't seem likely from what you say. that there is anything you can or should do to the insides of your Matrix. The change of mixer may mean you've changed the gain structure in this part of your setup, possibly the impedances are altered too.
Try comparisons with another one first, it may be normal behaviour in ths new setup, it may be some grounding issue within the Matrix, or a factory mod that hasn't been carried out correctly, or at all.
The leaking of generator noise is a feature of the Hammond by the way, we all love it, but some are worse than others, nobody persues this.
If you're determined to have a look, look for signs of poor connections to ground, have a look at the schematic, look at how many connections to ground there are and consider how the noise might be re-entering the audio circuits before you get the thing open.
This capacitor replacement fetish does have a basis in fact, old analog equipment tends to heat capacitors up, and modern equipment has in some cases been built with caps that don't quite do what it says on the tin for quite as long as we'd hoped. Substitution of parts often helps, but it's not where you start.

Unless your standard of workmanship is very high, and you're very careful and well organised, you're quite likely to lose what you have, a working keyboard, and gain a large bill for a much more serious repair.
The Matrix may or may not have a fault but I believe it's like your car, you need to take it to an experienced person. If you're lucky enough to find one.
The techniques required for repairs to synths are not something you're likely to find by accident and enthusiasm.
In the days of point to point wired hand made guitar amps, there was a chance to learn by doing without too much chance of doing damage, but the Matrix isn't that kind of animal.
Trying to fix it by guesswork, even communal guesswork with well meaning helpers, does sometimes work, but if it has a proper fault a proper repair is what it needs. I understand these talented repair people are hard to find, but the more people that make the effort to look for them and share their positive experiences, the more technical support people will stay in the business.

On a more cosmic level:
To get the answer, we must formulate the question.
Electronics fault finding is a What question, not a Why question.

Often the fault is something minor or imaginary,and with the casting of a professional eye you might get news of some impending disaster that will save you a small fortune, the rattling noise that's the mains transformer colliding with the main processing board after the bolts sheared off for example.

Turning up the drums isn't that bad an idea too.

--- In oberheim@yahoogroups.com , "eightiescrisis" <eightiescrisis@...> wrote:
>
> Recently upgraded my mixer, and now I notice my Matrix 6R is fairly noisy. It seems to have a low level noise and synth rumble on all the patches. What's unique is that the sound changes from patch to patch, but is always there. You can here it when the synth is not being played, and I've even removed the midi cable, and turned everything else off, just the module and the mixer........
>
> I guess I could turn the main volume down on the unit, but is there something else I could do
>
>
> Should I replace the caps, and where are they and what do they look like
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> Is this common
>