Hmm. Not to insult you, but you are aware that sys16 isn't standard jamma and needs an adapter? Also make sure the jamma connector of the supergun is lining up correctly with the jamma pins of the arcade pcb. Sometimes arcade operators file down the edges of the jamma connection which can cause alignment issues.
Sounds like either a short, which is activating the ATX protection and shutting down, or perhaps it's pulling more power than your particular ATX can handle.
When I'm at home I'll conduct some tests and measurements, I have some low power ATX and will see what happens.