I don't think it'll matter that you use the same computer.. I would be more worried about buying two sets of tickets to the same address to people with the same last name... I'm no computer wiz, but I think this might be something that the ticket people would flag.
I plan on purchasing a ticket for my gf and I with my registration info on my laptop, and I will also be on my desktop using my roommates registration and cc to purchase his one ticket. His CC's address is still connected to his former address (his parents address,) so I don't think that will get flagged, and I'm also no gamming anything here.. he's busy at work so I'm just doing what he would be doing if he were able to get the afternoon off work.
Can you at least admit that nuclear explosions are awesome!?