How are your programming the MCU? I didn't see an ICSP port. I see that MCLR is not connected to anything except for the reset button. You need a pull up resistor on MCLR to prevent spurious resets. Read the datasheet (See Page 151 for MCLR) for the MCU so you can properly wire up the MCLR and set up the ICSP port for in-circuit programming and debugging.
You also do not need to connect the RS232 RXout to the interrupt INT2. the UART module has an internal interrupt signal for triggering interrupts when Serial IO is received. Remember that Serial I/O is serial not parallel, INT2 will trigger for each and every Bit sent, not per byte!
I would also recommend some on-board status LEDs that you can flash using a couple of pins on one of the IO ports. This will help you make sure your MCU is running or performing as you expect. Its going to take a bit of trial and error before you get the UART working correctly if you are new to Microchip MCU's. So before you get UART working you can use the LEDs as status indicators.
I would google for some PIC30 schematics or look for Appnotes so you can see how to set up a PIC30 MCU. Schematic doesn't have to be for your exact MCU ie (dsPIC30F4013), any model in the 4000 series is probably close enough, for the common pins (MCLR, ICSP, Power, UART, etc).