I wouldn't recommend plugging or unplugging the IDE cable when the computer is on. That is a seriously bad idea. You shouldn't touch anything inside the case with the computer on. Besides, I highly doubt it would do any good even if it wasn't bad idea.
IDE devices are detected and configured at boot time by the BIOS, Windows doesn't do that.
I'm afraid your drive is toast. The manufacturer can probably revive it so that's a possibility. But it will most likely cost you, messing up as firmware update isn't covered by the warranty.
I'm sorry you had to learn this the hard way, but a firmware update is not to be taken lightly and shouldn't be attempted at all without good reason.
And when you do a update firmware be sure the computer isn't doing anything else, especially something that requires communication on the IDE cable. Many manufacturers also recommend you disconnect anything that is connected to the same IDE cable as the device you're updating.
I wish I could give you better news but this is the reality. Hopefully you'll be more careful in the future.