Hi, hmm if R4 was failed high ohms that is not a good sign, it means R4 was exposed to a sustained over-wattage situation (too much current through it). That excess current can only come through the IC via the output drivers in U1A, so it's very likely the IC is toast. I would replace the IC with R4.
Re the operation, there's one basic feedback mechanism; if the voltage drop across R4 is not high enough then the output of U1A is changed in voltage. The reason there are two branches in the feedback loop is because neither end of R4 is at a known fixed voltage, so the feedback measures 2 points to get the voltage between the 2 points, which then produces one feedback signal.
One of the analogue experts can probably explain the operation better than me but that's the basics of it.