I had to stop the web shield to gain internet access. Will this lower my protection level?
Yes it will.
It is very recommended to
not pause or stop the webshield, which can and does detect threats on sites that may have been hacked; have malware links embedded (usually in a hidden manner)in them.
Sometimes warnings from AV's such as Avast have been
the warning to site operators that all is not well.
In terms of general internet access, the problem in your case is likely to be firewall related, or related to a previous AV installed.
What firewall do you use?
What AV was on the system before Avast?