What do those various colors mean as the Amiga boots up?

 

When the Amiga boots, the screen changes color to indicate the progress of several internal tests. Here is what happens:

The first colors you will see are shades of gray .. dark gray, middle gray, light gray, and then white. The RGB color values are 0x444, 0x888, 0xAAA, and 0xCCC, in that order. Colors shown before the four gray shades are artifacts from the original values in the custom-chip registers and do not indicate a failure.
The failure mode screen colors:
turquoise (0x0CC) (A1000 only) RAM failure in the Kickstart WCS
green (0x0F0) error in the lowest 256 bytes of Chip RAM. Possible causes, defective CIA-A IC or defective Agnus IC.
yellow (0xFE5) an unexpected processor exception before the appropriate system failure message was prepared. This could mean defective hardware or an attempt to access a RAM address where no RAM exists.
red (0xF00) invalid KickStart ROM checksum.
magenta (0xF0F) single-task or cold-start initialization failed.

Here is another interpretation of the Amiga boot colors:
RED Kickstart ROM error Two ICs in A1200, A3000, A4000
BLUE Custom chip problem Denise Paula Agnus
GREEN RAM error
YELLOW Above problems combined
LIGHT GREEN CIA (U7/U300) problem
BLACK CIA (U7/U300) problem If not booting
DARK GRAY Hardware tested OK
LIGHT GRAY Software tested OK
LIGHT GRAY CIA (U8/U301) problem Stops at gray, CIA defective
BLACK/STRIPES ROM or CIA
No video R406 or R215 open R406=1 ohm R215=4.7 ohm
Video scrambled Agnus or Denise defective

If the Amiga caps lock key LED blinks repeatedly at boot up, another series of error messages must be consulted:
one blink . keyboard ROM checksum error
two blinks .. RAM failure
three blinks .. watchdog timer failure
and not part of the official specification, but observed by the keeper of this page:
on the A500, multiple repeated blinks indicate low voltage on the 5-volt line from the Amiga 500 power supply.