Hmm, so based on the math found on this thread's best answer, I'm ballparking the Nano current draw to be approx 33.4mA.
And then also this thread's best answer, it appears that I can draw 100mA from a new CR2032 cell.
If I ran just the Nano and a single LED (a configuration I also tested), and estimated LED at 40mA (not super bright so likely less than 40), my current draw should be roughly 73.4mA in this configuration. I also have two CR2032's in series. In this configuration, the single LED did not light up either. Is this rough test/assessment valid?
Are there other ways to get around this, with using the CR2032? The advantage of the CR2032 is the small space/volume.