Thin client built into the keyboard
Even thin clients for network use, instead of thick client alias stationary computers, are not as small as could be.
As you anyway have to use a keyboard, you could as well build the electronics into the keyboard as one unit. Perhaps you also could add an optical drive, now that you have the space in the keyboard. That will make the thin client even more useful.
You have to add power with a transformer cord from the wall outlet and appropriate I/O contacts in the back or at the sides of the unit.
A track ball could be built in as well, or you could use a normal mouse connected with USB.