I'm afraid not, we really need a schematic to see what's going on.
However, there is a schematic for a KRK RP10S, though there's no resistor of that designation. BUT, there are a couple of 270 ohm resistors, R338 and R339, which feed +vcc and -vcc to a pair of comparators (U3-A/B) which feed a muting circuit using FET Q6. Presumably this is to do with anti-thump?, as the amplifier turns ON and turns OFF.
So that resistor having burnt-up (I presume you've tried measuring it with your meter?, and it's O/C?) would mean the -vcc feed to the comparator is missing, so presumably causing it to stay muted?.
There's nothing in that circuit though that could cause R339 (the -vcc feed in the RP10S) to burn up, as it just feeds to a 47K resistor, so would need a short to ground from the output of the burnt-up resistor to damage it.
But that's just guessing, based on the RP10S schematic.