I'm not 100% sure, but it may be a CPU fan issue. Had that on one of my relatives' Dell laptop. Her fan wasn't working and it was constantly shutting down 1 ~ 3 sec. after boot. Since, the blue light shows normally until shutdown, it's hard to know what the exact issue is. If it was a hardware-related issue (HDD, graphics, CPU etc.) it would show something like the yellow light. Again, I'm not 100% sure, but check the fan. The whirring sound that you hear might be from the HDD or from a game disc that is in the drive. The Blu-Ray drive's sound is somewhat louder than the fan.

I don't know (since I don't use an iPhone), but it may be a software-related issue. Contact Apple Support and they will probably fix the issue.