its quite simple, and you've answered the question already yourself
you said...."It only happened if windows (V7) arrived at the log-on window before the router had finished initializing "
So, the computer isn't picking up a valid IP address from the router and is instead self-allocating a 169.xxx.xxx.xxx address - which will be invalid on the network. The PC will be attached to the network, but not part of the network. Once the 169. series address is used, that won't change until you reboot, or maybe repair the connection (thats not always reliable)
Its not picking up a valid IP address because the router hasn't booted to a point where it is able to allocate one
The answer?
Leave the router on all the time, as its supposed to be
Or if you really object to that, turn the router on first, go make a cup of coffee, then come back and turn the PC on