You're probably spot on in thinking that the disc drive's laser has been misaligned. Try unplugging everything and laying the Wii horizontally for a day. If it hasn't been misaligned terribly bad, this might reset it to it's usual position. Only a few people have had success with this method, though... Can't say it's reliable.
It sounds like the Wii was recently purchased, so unless you have reliable experience in fixing those past laser problems you mentioned, I'd highly recommend ya send it to Nintendo for a free repair if the laser won't reset itself. A week or two of waiting and a renewed warranty is better than risking said warranty and ending up with an unfixed Wii, I'd say. You can look into getting a repair set up here.