I don't know what the fuel pump on your car sounds like but the whirring might be the fuel pump - you probably wouldn't notice it running once the engine fired up.

+1 ??

Probably an extremely low, if not dead, battery. It does not take much current to run a few lights, a little more to drive a wiper motor, but it takes a huge amount to crank an engine. Put a battery charger on it and give it a long. slow charge to build the battery up.
Modern cars use electricity even when parked and will wear the battery down eventually.

If charging the battery does not solve it, get the battery load tested. That will tell you if the battery needs replacing. A battery can fail between drives on the same day, so leaving it uncharged for a couple of months might be more than just needing recharging.

I have a 2017 Cooper S that I haven't driven in a few months. I tried starting it and displayed battery low. The radio comes on and all the lights work fine. The wipers are a little slow, probably the low battery. And when I hit the ignition button it is making a whirring noise and my brake pedal seems to be stuck depressed. Any idea what is going on and any help will be highly appreciated. Thanks in advance.