ICD3 + PIC + MPLAB: Target Device ID 0x0 does not match expected Device ID
Edited per the updated information provided.

0x0 generally means no communication. Either a bad device, bad connections on the ICSP or power issues. I'll trust that your 3V3 rail 'works' for now.

Your _MCLR resistor and use of ICSP port 1 should pose no issue with the debugger.

Do you have sufficient decoupling, per the PIC24 datasheet? Decoupling capacitors must be installed as physically close to the PIC24 as the layout and pinouts permit:



You can see that for every \$V_{DD}\$ and \$V_{SS}\$ pair, you need a 100nF ceramic cap, and a 10 microfarad cap at \$V_{CAP}\$. What is shown in your schematics for the 3V3 rail doesn't appear to be sufficient, and more importantly, you don't have anything on \$V_{CAP}\$ (which is very bad.) Per page 20 of the datasheet:


  A low-ESR (&lt; 5 Ohms) capacitor is required on the VCAP pin, which is used to stabilize the voltage regulator output voltage. The VCAP pin must not be connected to VDD, and must have a capacitor between 4.7 μF and 10 μF, 16V connected to ground. The type can be ceramic or tantalum. Refer to Section 24.0 “Electrical Characteristics” for additional
  information.


Fix up your decoupling and let us know what happens.