Can't remove fork from head tube!

The OP describes that he has removed a conical thingie, which is probably the compression ring. If so, I don't think a pick will solve anything.

I would use a 2x4 as a buffer between the fork and the a mallet or hammer.. Just make sure your whack is good and lined up, and make sure the 2x4 is flush with the steerer tube.

Also, drip some oil or even penetrating oil on the steerer andand let it sit for a few hours. The oil is bad for the grease in the bearings so be sparing, and keep it on the steerer. A little bit will work its way in there and loosen things up. You could also use some oil on the bottom with the bike upside down, but that will probably wreck the bearing, since you won't have the same easy access you do at the top. You may want to be replacing the headset bearings anyway though.

Finally, depending on your work stand situation, you may need to adjust how the bike is being held. If you give a whack and the head tube moves, a significant amount of the energy is being deflected into the work stand. I did this recently, and found success by clamping the frame as close to the head tube as possible. I would not recommend this on a carbon frame. If that is the case, I think going to a LBS is essential.

Good luck.