Run a program on a PICKit 2 chip

You have to set the configuration bits. Near the end of the device's header file (line 5880 for dsPIC30F4013) is a listing of all the device's configuration bits that need to be set or cleared to ensure proper operation of the device, as well as code comments for how to do it.

For example:

_FOSC( XT & CSW_FSCM_OFF )  // Configure for external XT crystal oscillator, turn off clock switching and monitoring

The oscillator and watchdog timer configurations are very important.

EDIT: In your edited post you tried using the phase-locked loop option for the oscillator. You have to add the following code in your main routine in order to use an external oscillator + PLL:

/*
 *  Set up the PLL for full 60 MIPS operation (dsPIC33EP512MU810)
 *
 *  Fcy = Fin*K/2 --> 60MHz = 8MHz*K/2 --> K = 15
 *  K = M/(N2*N1) --> 15 = M/(N2*N1)   --> N2 = 2, N1 = 2, M = 60
 *  Fcy = 8MHz*15/2 = 60MHz
 *
 *  p. 164-171 datasheet
 */
void configPLL()
{
    PLLFBDbits.PLLDIV = 58; // M = 60
    CLKDIVbits.PLLPOST = 0; // N1 = 2
    CLKDIVbits.PLLPRE = 0;  // N2 = 2
    OSCTUN = 0;
    // Writing to the OSCCON register requires a special unlock sequence
    // Using a compiler built-in write instruction to handle this
    __builtin_write_OSCCONH(0x03);  // Select primary oscillator with PLL   
    __builtin_write_OSCCONL(0x01);  // Request oscillator switch
    while (OSCCONbits.COSC != 0x3); // Wait for the PLL to lock
}

The PIC may have been told to 'raise its shields' or may have been programmed to not respond to the programmer clock or oscillator control network. These problems are usually recoverable by following a suitable path. A circuit diagram of your target application may be useful.

Without looking at your specific PIC:

You may have code protection set.
The device should be able to be erased with code protection set.

You may have selected a clock type that the programmer does not support.
Worst case if it is not seeing your programmer clock or crystal you may have to uses ICSP with the PIC in a breadboard and supply a clock source or crystal or resonator or RC network or whatever that allows the PIC to run so it can listen to the programmer well enough to find its way home.

There is a small chance that it has been damaged in the process and is irrecoverable. Be sure to use adequate anti-static precautions and correct operating voltages, insert and remove with power off, ensure that no signal levels exceed absolute maximum values.