You are very brave to attempt such a repair as your first soldering job - the common problem most beginners make is too much solder and not enough heat - this leads to dry joints (may look OK but will not conduct electricity) and solder splashes forming an unwanted bridge between tracks - sadly these bridges are nearly always good joints and never dry ones!
Solder wick is a copper braid used to soak up solder when removing components - too long an application of heat may cause the track to "lift" from the base board - little at a time when unsoldering.
You are lucky that the AC adapter still works.
You should carefully inspect your work and if necessary remake it - it's quite possible that your efforts have caused damage but you might get away with it - you seem to have nothing to lose - I doubt you could make things worse.
The smoke will have come from high current flow making something hot - look for the scorching - use a strong light and a magnifyer.
Good luck...
Peccavi
January 2010
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