Eric,
You need the Device manager to show that you have a DFU device installed.
Using the Device Manager (DM), and with the nano connected, delete any STM bootloader device(s) shown.
Then, use Zadig to install the correct driver. (check the forum Wiki)
Once you see a DFU driver, you can flash the device.
As for your device stuck in DFU mode, turn it off & remove battery.
Check continuity from Boot0 pin to both Gnd and Vdd pin (NOT Vcc!)
-DO NOT- use an ohmmeter that has over 1V at the probes!
Without the Jog SW pressed, and with no jumper from Boot0 to Vdd, there should be no connection to Gnd or Vdd.
Some jog switches get stuck when pressed-inward causing a permanent DFU.
Good luck!
...Larry