Amber light

> [...] Solid white light becomes solid amber on my router [...]

   How many lights are there on your "my router"?  _Which_ "Solid white
light becomes solid amber on [your] router?

   Visit http://netgear.com/support , put in your model number, and look
for Documentation.  Get the User Manual (at least).  Read.  Look for the
LED descriptions.  Now that we know what "amber" means, ...

> [...] when desktop computer enters sleep mode. [...]

   On some computers/devices (such as your (unspecified) "desktop
computer", apparently), an Ethernet interface will run at 100MHz when
the device is in a standby or (not-truly) "off" mode.  When such a
device is awakened or powered on, it may negotiate a faster link rate.

   If the computer's sleeping, then how important to you is the speed of
its Ethernet interface?

> [...] Replaced Ethernet cable, [...]

   If the cable was good when the computer was powered on, then I'd bet
that it stayed good when the computer was shut down.

   Don't worry; be happy?