Be aware that if you connect an external keyboard and mouse then they will show up in device manager also.
Sounds like you have a Spin 1 convertible which is an update on my R3-131T. On mine there is a switch on the hinge and if you rotate the display past 180 degrees (flat) it goes into tablet mode and the keyboard/trackpad are turned off. A "tablet" icon appears briefly on the display. Rotate back to about 90 degrees and both turn back on and a keyboard icon appears briefly. Keyboard (PS/2) shows up in device manager either way.
How long have you had it and did it always act this way ? Any chance it was dropped on the hinge ? May be a warrenty item.
This appears to be a "feature" in the BIOS (would like to turn off for presentations with an external projector but never figured out a way).
ps <fn>-F7 turns the touchpad on and off but not the keyboard.