MPLAB X IDE problem with PIC Programmer
The PICkit2™ only has partial (i.e., beta) support in MPLAB-X.  If your PICkit2™ isn't a genuine Microchip one then chances are it won't work with the driver in MPLAB-X.

I have used for many years now a cheap PICkit2™ clone (one of the yellow heatshrink wrapped ones from eBay).  It works perfectly in everything else, but MPLAB-X won't work with it at all.

The PICkit2™ is now considered an end-of-life product and as such they haven't spent much time or money porting the driver to MPLAB-X. They have done enough to support the basics of the official ones, but not enough to make it work with other's clone devices.

It may, in part, have been an attempt to curb the use of unauthorized clones and drive up sales of official ones, but that's probably just the cynic in me talking.

I always use pk2cmd or pic32prog with my PICkit2™ from the command line - both work flawlessly.  If I need to program or debug direct from MPLAB-X then I use a PICkit3™ instead.