Hi.
If you are using an ethernet cable from the SAME laptop to check your
router, then yes, the wireless will, by default disconnect from the
router when you plug in your ethernet cable anyway. Make sure it's a
different pc you are using to check the laptops wireless connection
to your router.
Fine, possible false test but not important.
I've had the same problem in an environment where there is no
interference. Appears to be connected, but no ping to router. Repair
works as does going into services and restarting wireless zero
config. In my case am pretty sure it's on the laptop's end.
So do some swapping out to see. As John said, try the laptop with
it's built-in on other APs or hotspots to see how it performs then.
Also, you can get a cheap usb adapter and see if you have the same
problem on the same machine with a different adapter.
Another thing: is there any correlation between this problem and
hibernating or shutdowns?
Just for kicks, I would be uninstalling and reinstalling the client
drivers and utilities with generous restarts. Clean it all out of
there and start again.
Also it may be a windows thing, and something needs to be rebuilt.
Sometimes installing another wireless adapter (USB adapter) and then
going back to your built-in will toggle something in Windows.
Steve