I'm not sure why TS (or TRS) to XLR cables are being used at all. The JBL 305P MkII has a TRS input. Just use T(R)S to T(R)S cables. Although I am also unclear why the signal isn't getting through with the existing cable.
Just to confirm, when you don't have the cables plugged in the sound plays through the Roland's built-in speakers normally, yes? Also you don't have anything plugged into the headphone jacks, as that will mute all other outputs, right? Are the headphone jacks 1/4" (6.3mm)? If so, have you tried connecting to one of those to see if you get any sound that way?