I often faced similar problems with noises from various sources. I cannot guarantee, but hope that my advice will help.
To be absolutely sure that nothing else but your Triton (or whatever other device) emanates the noise I'd recommend that you take good care of connecting it to a well-grounded wall outlet as the only device (no powerstrips/multiplugs, etc.). Remove all other connections to the synth. For connecting audio use only the necessary one or two direct audio cables and connect a BATTERY OPERATED headphone or power amp to the audio output (similar to Sparker's case with the laptop in his earlier post). Obviously try volume pots at both extreme settings, also on your battery operated amplifier. Another word of warning is to watch for the case not touching another metallic object (e.g. the stand). This might also be the source of noise, so you should place a blanket or similar underneath the instrument to ensure perfect electric decoupling.
If you still can hear the noise in this configuration (wheter dependent on pot settings or not), you have a good chance that your device should be taken to a repair shop. The reason can be bad shielding, bad solder, fading caps in the grounding or the power supply filtering, etc. - too many to give a simple diagnosis.
If however, this makes the noise go away, then you know your homework: find the culprit by reconnecting/reinstating one by one the elements to your setup.
Just to give you an example: my Yamaha CVP made strange clicks when played - just at the beginning of the notes and when keys were released. It turned out to be the the seial port that was connected to an inactive computer. It somehow reflected the signal sent, and this made its way into the audio output. Serial cable disconnected - problem gone. Same with USB ports, very often I experience noise problems when something is connected, in particular so with a computer or other device with switching power supply - but sometimes even 'passive' devices (e.g. pendrive) will add noise.
Remember that the only electrically decoupled connectors on a musical instrument are the MIDI IN port (if done properly - which it usually is) and the OPTICAL (TOSLINK, ADAT, etc.) digital inputs/outputs - if there are any. Other digital connectors (COAX, AES) are sometimes decoupled also, but unfortunately this is not always the case.
BTW, the noise in the mp3 few posts earlier sounded very much like digital electronics maybe with an added whine from an inverter (backlight?), so if the noise persists when the Triton is isolated from everything else I'd start looking at grounding within the box or check caps (particularly in the power supply). Just repaired an old computer in which caps gave in gracefully (well, sort of)... Read this (affects mostly electronic devices manufactured between 2000-2005):
http://en.wikipedia.org/wiki/Capacitor_plague