My old 2011 iMac quit on me. About a refurbished same model The old mouse and keyboard is not communicating with a new computer, So I am not able to initiate the computer. How do I do that?
My replacement 2011 iMac had BT difficulties so I got a BT dongle for it. HOWEVER... dongles aren’t recognised on initial reboot so I have to use a wired mouse, go into a non-password protected user account, click System Preferences/Bluetooth, then switch on and pair my BT mouse and keyboard. I can do all that with just a mouse and no keyboard.
Your issue may be different, but you should start with a wired mouse then try to pair your BT kb / mouse as per above.
By the way, a Magic Mouse DOES have an LED - it's on the base just above the on/off switch. Steady green means it's on, also when it's paired. Flashing green is when it's trying to pair with the Mac.
My replacement 2011 iMac had BT difficulties so I got a BT dongle for it. HOWEVER... dongles aren’t recognised on initial reboot so I have to use a wired mouse, go into a non-password protected user account, click System Preferences/Bluetooth, then switch on and pair my BT mouse and keyboard. I can do all that with just a mouse and no keyboard.
Your issue may be different, but you should start with a wired mouse then try to pair your BT kb / mouse as per above.
By the way, a Magic Mouse DOES have an LED - it's on the base just above the on/off switch. Steady green means it's on, also when it's paired. Flashing green is when it's trying to pair with the Mac.
Are the Mouse & KB USB or Bluetooth?
If then you have to unpair them.
If USB try a PRAM reset, ...
Reset NVRAM on your Mac - Apple Support
In fact, do 3 in a row, takes a bit of time.
Intel-based Macs: Resetting the System Management Controller (SMC)...
Reset the SMC of your Mac - Apple Support...
I'm a little confused by your question. Are you unable to control the 2011 iMac with either a mouse or keyboard? Did they both stop working at about the same time?
There are no visible LEDs on the mouse, but the wireless keyboard that came with those Macs at the time should have a green LED on the right that illuminates when you press its side button.
Try replacing their batteries.
Those older input devices do not work with newer M series Macs.
Mouse not communicating with computer. No green light on mouse.
