Somehow I've got myself a "WTF" dilema with my newly setup Turntable. HELP!

I propose you are confusing the setting for your cartridge.  You have a high output MC cartridge which will require the same gain setting as a MM cartridge.  So that means a low gain output setting.  

You refer to to a high output setting which is the exact opposite of what you want with a high output MC.  I looked up the spec for your phono stage and it provides a whopping 85 db on high and even a seriously high 60 db on the low setting.  Most phono stages provide 40 db low and 60 db high.

 I think you are overloading the input on the preamp.  Try the lowest gain setting.

Try the phone IC into Left of Aux and Right of Tuner. See if switching sources still plays audibly.
Trying to ascertain if the pre/power amp is loading the phono amp incorrectly - i.e. a phone amp issue. If it does play on one channel for both sources and not when both are in one source input, I'd suspect the phono amp.

Typically, the choice of gain setting is made at the input side of a phono stage.  Many/most that provide both MM and MC levels of gain provide corresponding "MM" and "MC" pairs of inputs.  This makes sense, because in nearly all cases, the major portion of the gain is created at the first gain stage after the input, so that the RIAA correction can be effected with a higher level signal than would otherwise be the case.  This is only to say that I would be surprised if the OP's phono stage has more than one pair of output jacks per channel, and if selection among those choices has an effect on phono gain.  But only the OP can say.

Among the hypotheses offered, I think the "channels out of phase with each other" explanation makes a lot of sense.  In that scenario, each channel would work fine if the other channel is not connected or not producing signal.  No doubt we will soon know whether that explanation holds water, because it's so easy to test.  Even more trivial explanations could work: (1) Internally broken IC that is creating an intermittent problem; (2) "Iffy" contact between the hot pin of one IC and either the output jack of the phono stage or the input jack of the integrated; etc.

Thank you rhljazz, You were absolutely RIGHT! I set the dip switch as if
I were setting up a MM cartridge (low gain) and it works great. rhljazz,
you were cutting it a little bit short though, My wife is enroute to the
airport to pick up her inlaws, and the husband is interested in what a
decent current turntable sounds like. Now I can show him.
Thank you ALL for any input and suggestions you may of had.
And thanks to this forum, it has helped me in the pass, and probably I will
need some assistance in the future. MERRY CHRISTMAS to you all.

Great call, Rhljazz!

FWIW, in most situations in which an LOMC gain setting is inadvertently used with a high output cartridge, I would expect the symptom to be severe distortion on musical peaks, caused by clipping in either the phono stage or the input stage of the preamp or integrated amp. And I would expect it to occur on musical peaks regardless of whether one or both output channels of the phono stage are connected.

In this case, though, perhaps what was happening is that when both channels were connected to the amp the resulting overload was triggering one of its self-protection mechanisms. And perhaps the symptom followed the interchange of channel connections because the signal happened to be a bit louder at the particular time in one channel than in the other. Or perhaps a minor gain difference between the two channels was the reason.

For the benefit of others who may read this thread, one thing it makes clear is how important it can be, when seeking help on a problem, to state exactly what equipment is being used.

Enjoy! Regards,
-- Al