It took me quite a while to figure out what was happening and why I couldn't get anything to affect that pin. (Just use a sharp object to gently press in on the metal you can see on one side of the connector and gently pull the wire out.) I couldn't find a clear explanation of what this connection's purpose is and I needed that pin, so out came the wire. The PIC-KIT3 actively drives this, so you can't use it as either a GPIO or PIC peripheral connection unless you remove the PIC-KIT3's wire to pin 6 on the connector. Beware of pin 6 on the ISCP/ICD connector! On the LPC Demo Board it's connected to the PIC's RA4. I'm going to borrow some of my daughter's fingernail polish and fix this for real. The connectors on my PIC-KIT3's cable have a little '1' embossed on the plastic but that's NOT the ICSP/ICD connector's pin 1.

The PIC-KIT3 connector's guide tabs should be towards the PIC on the LPC Demo Board (the smooth side of the connector should be closest to the edge of the LPC Demo Board). The connector that came with the Olimex PIC-KIT3 won't plug into that right-angle connector - you'll have to replace it or gently/carefully bend it up to a better angle. My 18-pin Demo Board used a 6-pin right angle ICSP/ICD connector. I'm not sure which specific PIC you're using but make sure it's inserted correctly in the LPC Demo Board's socket. Be very aware of the PIC's voltage - is it 3.3V or 5V? Set the PIC-KIT3 accordingly.

Don't power the board with the PIC-KIT3 - use an external power supply. Your LPC Demo Board is very similar to the 18-pin Demo Board I'm using, so hopefully these suggestions will help:

Pickit 3 pinout to 28 pin