mac wireless keyboard not working on boot up

The iMac can be awakened from sleep with keyboard and mouse. I never understood this, I assume it indicates that the keyboard is detected. The 1 st checkbox is 'Open Bluetooth Setup Assistant at startup if no keyboard is detected'. I checked System Preferences → Bluetooth → Advanced. By doing this repeatedly during startup as soon as the light went off, I got the startup options once. After that, the light goes off and can be turned back on for a few seconds by pressing switch on right side of keyboard. After that, the light goes off and can be turned back on for a few seconds by pressing switch on right side of keyboard. The green light on keyboard comes on momentarily during startup, so the iMac must be communicating with the keyboard. The green light on keyboard comes on momentarily during startup, so the iMac must be communicating with the keyboard. I replaced batteries in keyboard and mouse, installed OS X 10.7 Lion, reset NVRAM using USB keyboard - Still same issue. The wireless mouse works to move the cursor to the text box and the wireless keyboard works to enter the password. From that point forward, everything worked normally. See the logs or run Apple Diagnostics(boot while holding down D key using an External Keyboard). It doesn't not require an external key board.

I can reset SMC using built-in key board and MagSafe power adaptor. When I selected a drive with the USB mouse, it asked me for a password. With a Magic Mouse and Keyboard, I can boot the Mac using all start-up options as well as reset NRAM(PRAM) mentioned in Apple KB. The wireless mouse was inactive at this time. When I attached a USB keyboard and mouse and started up with the ⌥ alt/option key down, I was able to choose between the internal drive and backups on external drive. When I started up with ⇧ shift or ⌥ alt/option key down, the computer starts up from the internal drive. I bought a wireless keyboard and mouse at same time. I have an iMac 21.5' (late November 2010, OS X 10.6.8 with latest updates).

Mac wireless keyboard not working on boot up