Gfci tripping when I turn on a tv on a different circuit!

Really this is happening. When I turn on a plasma tv upstairs a downstairs Gf I trips! Tv cooke's on just fine!
The gfci that is on a different circuit trips only when the tv has been used for at least 20 hours or so. If the tv is quickly turned back off and in the other circuits gfci does not trip!
There is a long run of outside wire to a shed and to an outside lamp post. Sometimes in heavy rain the gfci trips and reset can not be done unt it dries out Wiring is 1940 BX but outside wire is newer plastic!
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