That sounds very much like the power supply not able to provide enough current.
During the cold boot the demand is highest. During reboots the hard drives don't spin down (lower needs).
Have you added/replaced drives lately? What does the 12V rail provide under load?
A good test would be to disable network in BIOS but connect the Cat6.
If it is just power shortage it should boot up just like it does without the Cat6 (no power supplied to the connector).
If it is a short, it won't boot up...
Diogen.