You can use Secure Settings Hardware Keyboard Action to toggle the hardware keyboard. Interestingly, you can still use the hardware keyboard, but the on-screen keyboard still appears.
This is especially useful when you connect a mouse (and no keyboard) and it causes the keyboard to go into hardware keyboard mode.
The simplest way to do this is to create a shortcut on your homescreen. Select the Secure Settings shortcut/widget. Then it will prompt you to select the action. Select Actions > Hardware Keyboard. Then it brings you to a screen with three options: On, Off, Toggle.
On means you go into hardware keyboard mode and no on-screen keyboard will appear. Note, this only works if you actually have physical keyboard connected. It will simply give you an error toast if you don't.
Off means turn off hardware keyboard mode, and an on-screen keyboard will appear when you select text boxes.
Toggle means it will switch from whichever hardware keyboard mode it's currently on.
There are other ways to hook up to Secure Settings Hardware Keyboard Action, which you can learn about in the documentation, and using your imagination and research.