Ok, so to draw a little bit of a picture with words, the start cycle is basically:
- Pump fuel
- Rotate motor
- Intake fuel/air mixture
Note that the above is not necessarily in that order and there are some nuances left out.
However, of the components involved in the ignition cycle, most are in the engine bay (engine, starter, ignition system etc). The only component involved in engine starting at all that is located near the rear, is the fuel pump. So this could be the culprit, however it is most likely not the source of the whirring/humming noise. The fuel pump will only operate when the ignition is in the "on" and in some cases "acc" positions, but almost never in the "off" and certainly not the key out position.
There are a couple other possibilities that could create a sound like that which have nothing to do with you engine issue. The 2 that come to mind are power antenna being stuck (odd that the sound would last so long but I have seen this several times in vehicles as the culprit of a phantom whirring noise) or possibly air suspension if the package is installed.
Now if we consider only the engine not starting, there are a few possibilities.
- Not getting air/fuel for combustion
a. Valves could be a factor
- Not getting spark for ignition
- Starter not actually turning motor
You said the starter and power checks out, so we can theoretically eliminate #3.
It is possible that it's not getting air/fuel, but that would usually have other attributes as well.
If it's not getting sufficient spark (little or none or wrong timing) it may also not start (or worse).
What it comes down to in my personal experience debugging no-start scenarios is what does the motor sound like. Is it a dry raspy spinning sound or a wet chugging?