ZSE Controller described a confused Data Block event when a VFR aircraft cycling through an IFR arrival's beacon code resulted in erroneous information being displayed.

Narrative

Aircraft X VFR was flashing hand off to Sector 6 and DATA was flashing as well. Associated with the target was a Aircraft Y Data tag. From talking to SEA Approach; apparently Aircraft X had cycled through the Aircraft Y assigned code and since Aircraft Y had just touched down and was not tracking anymore that data tag jumped onto Aircraft X. When Aircraft X finally got to his assigned code we had two data tags on the same target. I could see where the Aircraft Y data tag was showing Aircraft X's altitude and Aircraft X's altitude was not showing. Tried to move the Aircraft Y Data Block but it was not my control. Aircraft X finally went into coast mode and I could not get it to track back up because of Aircraft Y. Had to remove strips on Aircraft Y in order to get Aircraft X to track normal. Having two data blocks tracking one target is just flat out wrong; unsafe and should never be allowed to happen. Recommendation; change the parameters to prevent this type of occurrence from happening in the future.