Just for starters, a few questions: 1) What iMac (year) are you using; 2) Did this problem start after a Yosemite upgrade; and 3) Assume you are now using a 'wired' KB - correct? Have you recently upgraded OS X and/or switched from a wireless to a wired KB? Might get the discussion started - Dave
I have the latest iMac 27" desktop, purchased in August 2014. The problem is unrelated to the OS as I started w/ Mavericks, upgraded to Yosemite as soon as it became available and have upgraded to the latest version of Yosemite. Apple at first thought it was a defective keyboard but no such luck.
Well let's put it this way. Ever used wireless on it, keyboard, mouse, printer or Capsule, or was it set up in an Apple store and running there? If so Bluetooth may be switched on. Go to System Preferences > Bluetooth > Bluetooth Off setting.
Be intersting to see if anything is listed under Devices there.
Something is not right with your setup. I have the same machine you do and my bluetooth is on. Yet I use a wired keyboard and wired mouse. But I receive no warning that BT is searching for a keyboard or mouse. What I suggest you do is a NVRAM reset, and if that doesn't work, do a SMC reset.
Since you have both a wired keyboard and a wired mouse, you don't use Bluetooth. I have a wired keyboard but a wireless mouse. Bluetooth recognizes this i.e. only the mouse is shown as a wireless device. Nevertheless, I get the message that Bluetooth is searching for a wireless keyboard. This is inconsistent as otherwise I could never start up my machine. Sometimes I have to try 3 or 4 times which is, of course, unacceptable.
PS: my Mavericks iMac's com.apple.Bluetooth.plist lists two devices that I have no idea what they are and I don't recall using any BT device, and even with BT turned on I have no trouble starting up and the settings as per chasm_m's screen shot above are all enabled.
I guess one could avoid the BT trouble when booting and to just not shutdown and just sleep the iMac. ;D
As I'm not sure what NVRAM and/or SMC actually do, I'm hesitant to try your suggestion. However, when I call the Apple technician assigned to this problem, I'll pass on your suggestion. Thanks, Nancy B