imac - all input devices stop working

I have a 4-month old iMac which is running completely up to date OSX 10.10.4.

Model Name: iMac

Model Identifier: iMac14,2

Processor Name: Intel Core i7

Processor Speed: 3.5 GHz

Number of Processors: 1

Total Number of Cores: 4

L2 Cache (per Core): 256 KB

L3 Cache: 8 MB

Memory: 16 GB

Boot ROM Version: IM142.0118.B11

SMC Version (system): 2.15f7

On two occasions, the latest just now, all input devices stop working. Both bluetooth Trackpad, and keyboard become unresponsive and nothing will revive them. Turning them on/off, resetting, etc. Nothing.

The first time this happened, I had to cold-boot the system by holding down the power switch until it shut down.

Later on, I remembered that I had a working USB laser mouse which I thought might come in handy if this ever happened again. I tested the mouse with the now-rebooted iMac and it worked fine.

Now today, both the trackpad and KB stopped working again. Now, here's the weird thing: I plugged the USB mouse in, and its laser light didn't come on! I know it works because I tested it after rebooting the first time. Even stranger, the USB extension box I'm using has LEDs that show power coming from the iMac. Those lights were on, but the mouse laser wouldn't come on.

So, hard power off, cold reboot again. Plug in the mouse, laser comes on, works fine, as do both KB and trackpad.

Is there anything that could explain this total stoppage of input devices?