First thought would be that the the router didnt connecct properly with the bridged gateway.. that you were getting a connection to the router.. but it wasnt talking out through the modem.
What is odd, is that it by reseting the network adapter (which is essentialy disable then re-enable) it does connect. Since its not touching the router.. it MAY be the PC?
Here is a test, if you are able to do it.
Try a WIRED connection, and see if you get internet ok. Try it with a fresh startup of the computer, etc.. and see if you are able to get out.
this may lead back to something on the wireless as a whole.