iMac keyboard & mouse not working

Both the keyboard and mouse to my new iMac quit working all of a sudden. I changed the batteries on both and it still won't work. On the mouse, when I turn it off and then back on I get a green light. Then the green light begins to blink on and off. But there is no response from my iMac.

Another thing that may be related: I can't find the bluetooth software on my iMac anymore. If bluetooth has somehow disappeared that means the mouse and keyboard can't connect. correct?

If anyone could please offer some advice, I would be most appreciative.

Have you tried using a wired mouse or keyboard and then backup and restore your computer?

I haven't. Is that the only to fix the problem?

Open your System Profiler application: Click on the Apple in the upper left of the screen, click on "About this Mac" and then on more info. Highlight the Blue Tooth entry. What does it say?

If the BT entry is missing, do a PRAM - NVRAM reset and also a SMC reset.

If neither of the above work, make an appointment with your local genius bar at the Apple store to have your iMac looked at. If the BT radio has failed for some reason, Apple will repair it under the warranty.