Just a guess(latch) purple constant live white grey switched live?
Try leaving connected run a additional earthing wire to pin 3 ( black latch) and press the remote boot button?
See what voltage is on pin 2 latch if zero see if it goes up when you press the remote button (a analogue meter is best for this)

Also

Is the roof properly closed? Fully open it and try the boot, fully close it and try again, often convertibles don't like the boot being opened if the roof is anywhere between opened and closed, not something I can imagine the 500c suffers from but you never know if it's been done as a fail safe

Sorry please note the diagrams are for the standard 500 not the cc

There is a link between the 500C roof and the boot as AndyRKett suggests. Just to be sure I'd suggest you do a roof initialization to eliminate the possibility of the computer being 'confused'.

With engine running and roof fully closed, press and hold the OPEN button until the roof is fully open, continuing to hold the button down for two seconds more before releasing. Then press and hold the CLOSE button until the roof is fully closed, again holding the button for two seconds more. The roof will (or should) then go through an automatic open/close sequence. That's it, then try the boot. Even if it makes no difference you'll have eliminated one possibility.