that's most likely the source...
focus on outboard PSU/connections, video leaking is quite unlikely.
For a start setup a project with open analog inputs and apply enough gain you hear noise.
Remove all external connections from the Luna Box.
Then unplug the powersupply of your Display - it probably didn't change anything.
If it did (unlikely), reverse it's plug in the main outlet (or it's wallwart).
Improved or not ?
If nothing changed, you can (mostly) ignore the screen display while searching on.
Basically you apply a similiar procedure to the Luna's PSU.
(for simplicity all gear should be fed by the same outlet... otherwise the number of variables may increase significantly)
If reversing the plug doesn't change anything, check grounding of the Luna and the PC case.
Btw is the box supplied via Firewire or via wallwart ?
if nothing is connected to the box and supply comes from the PC, there shouldn't be any significant level of noise
(a little bit is always present of course)
it's most likely that the noise increases when you connect outboard gear to the Luna box.
In that case treat supply accordingly and check how each device is grounded.
To give you an impression how far such stuff may reach: I once had a fairly 'clean' setup... until I connected a coax S/PDIF cable from another PC to the amp driving the monitors. That loop folded back into Scope's analog IOs
good luck, Tom