There is no doubt that the sound coming from your rokit is sign of a shorted power transistor inside the IC.
It's your choice, you can buy some of the cheap 2052 from ebay and hope that you get a good IC or from a UK seller which is expensive or replace it with the 3886.
When replacing parts and when your in doubt, it is good to test the circuits before the main amp (tda2052) that it is in good working order, one way to check this is to feed its output to a good know working amp (this is where the headphone amp comes in), you can also check it using an oscilloscope if you have access to it.