I'm not used to having a floppy drive on an XP machine.
I plugged in a NEW floppy drive, which I just got in the mail. I used
that twist cable which I mentioned. (twist on drive end), and connected
the power cable. Everything is plugged in properly.

I am not seeing the A: drive in My Computer.

I am not sure where else it should show up.

I confirmed this drive works by plugging it into the existing cables
connected to the internal floppy drive and it works fine. I read, wrote
and formatted a floppy.

In XP, I went to control panel, hardware, and I can see the floppy
listed. It says it's working fine.

I went to the command line, and typed A:
It says "Invalid drive specification".

The only thing I can think is that maybe that cable is defective???