Curiously, the PS/2 scan codes for power (E0 5E) and left GUI (E0 5B) are very similar, and although you're using USB, Filco keyboards understand both PS/2 and USB. It surprises me that you'd see ctrl+alt+del+enter appear in the on-screen keyboard since it's a fault with the keyboard, I have to wonder if that's the on-screen keyboard's way of showing the power button.
What happens if you change the Windows settings for the power button so that it doesn't do anything? Supposedly that setting covers both the front panel button and the keyboard button. (If the controller is sending the wrong scancode you could see if SharpKeys will let you remap power to left Windows, at least until you get a replacement controller : )
I'm guessing controller failure of some kind. My Poker II at work keeps adding ctrl to keystrokes at random that may, too, be a controller fault. I don't have a good spare keyboard to use in its place to see if the fault disappears (I don't have much with a proper modern layout!)
Disabling the power button has stopped the key from shutting down my computer! I was able to save my output from SwitchHitter and the key doesn't seem to be sending the same codes each time it is pressed:
55:29.0109 F7 (0x76, BIOS 0x41) DOWN
55:29.0109 [ (0xDB, BIOS 0x1A) DOWN
55:29.0109 Backspace (0x08, BIOS 0x0E) DOWN
55:29.0109 Numpad 4 (0x64, BIOS 0x4B) DOWN
55:29.0109 Numpad 5 (0x65, BIOS 0x4C) DOWN
55:29.0109 Numpad 6 (0x66, BIOS 0x4D) DOWN
55:29.0109 F7 (0x76, BIOS 0x41) UP -> 10ms
57:47.0816 Backspace (0x08, BIOS 0x0E) DOWN
57:47.0832 Numpad 4 (0x64, BIOS 0x4B) DOWN
57:47.0833 Numpad 5 (0x65, BIOS 0x4C) DOWN
57:47.0835 Numpad 6 (0x66, BIOS 0x4D) DOWN
57:47.0838 Backspace (0x08, BIOS 0x0E) UP -> 8ms
57:47.0838 Numpad 4 (0x64, BIOS 0x4B) UP -> 7ms
57:47.0838 Numpad 5 (0x65, BIOS 0x4C) UP -> 8ms
57:47.0838 Numpad 6 (0x66, BIOS 0x4D) UP -> 7ms
59:15.0320 Tab (0x09, BIOS 0x0F) DOWN
59:15.0535 Tab (0x09, BIOS 0x0F) UP -> 208ms