These are most likely two different problems or the same problem. Try this, when you don't get the logon script try pinging one of the Domain Controllers by IP, if you are succesful try pinging it by name, if both work then most likely the Domain Controller you are authenticating too does not contain the login script file, you can verify which is the DC that authenticated you by typing "set L" at a DOS prompt, then verify that server contains the login script. If you are succesful with the ping by IP but not by name verify your DNS entries or your DNS serever it self (WINS also if your using it). If pinging fails this would answer your second post, problem could be a bad network card, network cable, netwok port, or incorrect drivers, problem would be local not at the Domain level.
Hope this helps.