At what point IS it a new computer?

This is the modern version of the Theseus Paradox, really; if I replace the video card, the memory, the hard drive, the CD drive, the motherboard, and then finally the casing – at what point did I replace the “computer?” Easy to pick an arbitrary point, like ‘motherboard’ or ‘casing;’ but what makes those acts of replacement significant.  if I started off by replacing the casing or motherboard, would it be accurate to say that that still represents a full replacement?  And if the act of replacement is time-dependent, then is there a moment in the process that can be said to be the moment of actual transformation?

I have not a clue, but my wife and I found it an interesting enough discussion topic on our way to the mall. Plus, it distracts me from the fact that I want a 2TB SSD, and I ain’t getting one any time soon. Those things are hella expensive, huh?