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It happened to me with the original singstar, phoned the sony helpline and they said I should get in contact with who sold it to me.
I got it from SR so just sent it back (Full game and both mics) to their returns department with a letter telling them that the mic wasn't working.
Got sent a new copy which worked.
The mics are a bit sensitive though, one of mine seems to have a loose connection so it works sometimes then stops for a bit.