Raspberry Pi 3; new user so please take nothing for granted.

Transfer a fresh image of Jessie to a 16 GB microSD card via
Win32DiskImager. Plug the card into the Pi; boots fine.

Change the configuration, or don't change anything at all; it doesn't
matter. Shut down via the GUI, then remove power.

Don't touch anything; just power up the Pi again. Red LED shines
brightly; several flashes from the green LED and then no more.
Completely blank screen (the monitor never even comes out of standby).
No boot. Try again several times; same story.

After this problem, if the card is plugged into a Windows computer (to
transfer the Jessie image again) it immediately triggers a CHKDSK, so
somehow the FAT portion of the file system is being corrupted by the Pi.
However, CHKDSK reports that it found no problems.

This happens with two different SD cards from two different
manufacturers (Sandisk, PNY).

What am I doing wrong?

Thanks.

--- SoupGate-Win32 v1.05