then you are good!
there is a piece of silicone under the coil. If you pushed too far with the philips head, you may have pushed the coil down so it contacts it. You can see there's quite a bit of room though between the top of the post and the coil. After you dry burn the coil and wick clean, just drip on the wicks at give it a moment.
If it's burning the rubber piece below, you'll know very quickly by the second/third puff. Treat your first few puffs like you would an atty when you are making sure the primer fluid is all gone and don't inhale unless it tastes clean. There is a definite difference between the taste of some left over crud on the coil and burning silicon. If it still tastes burnt, repeat the dry burn process. If it tastes like burning rubber, you may not want to fill it up. Without taking it apart to rebuild it may be a loss unless you can get in there with the bent paperclip and pry up the coil a little. It can be as slight a pull as wiggling up the center post to make contact with the battery.
Of course, I don't know how aggressive you were at trying to take the post out. If it wiggled at all, you my have damaged the base and you will want to leave it for awhile after you filled it to make sure nothing is leaking.
Sometimes, your first time doing these things has to be a learning experience.
I'm just posting this because I'm headed out for the night and won't be here. But I'm sure it will be a success!