I've had success on several laptops taking the cotton off the end of a q-tip, and sticking the bare q-tip end in the jack, applying slight pressure and twisting it around a few times.
Make sure to do this kind of thing while the power is off, especially if you're putting metal objects in there.
Many laptops have long lives after this issue has been fixed, and with no recurrence of the issue, so I don't agree with the assessment above that the motherboard needs to be replaced.