>>The problem seems to be the crystal. It doesn't oscillate very well.

<snip>

>>- when I touch the GND side of the caps with my fingers, sometimes the led
flashes up.

I had the same symptom once before.  I did not have the configuration word
in the hex file and I failed to notice that the PICSTART+ oscillator
configuration box defaulted to RC instead of HS.
It was a little confusing at first.  I had one prototype (programmed
correctly)  that worked and about 15 first run units that did not work with
no apparent physical difference. :)>

Hope this helps,
Jonathan

P.S. I've lurked long enough... I suppose it's finally time to attempt to
contribute to this incredibly useful list.