It is possible that the USB Cable is still not correct. A new COM# should show up when the TinyDuino power switch is ON (it may help to double-check this), and when the cable is working. You can check that the cable is working by opening the Device Manager and plugging and unplugging the device, as seen here:
https://learn.tinycircuits.com/Help/Port_Trouble_Tutorial/On Windows 10, you should not need to download any drivers - separate downloadable drivers are only noted for Windows 7 users in the TinyDuino tutorial.
You should not need to remove the device on COM3 if you have more USB ports to plug the TinyDuino into. From the Arduino IDE Tools menu, you will need to manually select the correct port to program the TinyDuino. If no other COM# is showing up, you can try unplugging the Prusa device and using that port instead.
To test that a Micro USB cable had all the data wire connections necessary to use with an Arduino device, you would need to verify that the cable can transfer data. So testing the cable with a phone or camera that is able to transfer data, like pictures, would be a good test.
Additionally, an LED should come on and blink green (I believe this is the code that TinyDuino's ship with), and that would not help determine if the cable is correct. You could also plug in a battery while the TinyDuino is plugged in and an amber LED would light up to show that the battery is charging.
I hope that helps!
Réna