I wouldn't worry so much about the firewall if you have a hardware firewall, BUT...I don't see how Windows Firewall could be the problem if you EVER had connectivity.
How would it intermittently only stop the connection when a computer was rebooted. I mean a fireall port is either open or closed.
I can't prove this, but I think the whole Windows can power off the NIC card thing doesn't do much.
To backtrack a bit, firewall and especially suites are big players in these issues, but again, not intermittently. But, isn't it ironic that we talked about Norton. You really should know if Norton has a firewall or not. It is either Norton Antivirus or Norton Antivirus/Firewall/Whatever else suite. Look in Add/Remove Programs or Programs and Features. Do you have the box or the download? I would just get the free version of Avast or run MBAM and take off Norton.
Have you had mapped drives before Sandeep recommended them?