How to connect a dsPic30f2010 to pickit3 icsp
You really can't expect things like this to work without proper bypass caps in place.

Make sure you have all the Vdd, AVdd, Vss, and AVss pins connected, and of course a bypass cap for each Vdd and AVdd pin.

Try putting 100 &Omega; in series with the PGC and PGD lines physically close to the PIC.