The network shield has no interaction with your browser.
The whole situation sounds more like a clash to me so you can't pin it down to a single element, it takes two to clash.
With a personal firewall, antispam, and the same antivirus and antispyware protection delivered by ESET NOD32® Antivirus, ESET Smart Security is the most comprehensive defense against Internet threats.
I don't know exactly what ESET smart security does, but there is every likelihood that a clash it possible as it has, an anti-virus (not recommended to have two resident AVs installed) and also a firewall (which could possibly be blocking the web shield, though it should also block IE).
I also don't know if uniblue spi eraser might not clash with the network shield as SPI is a term related to packet inspection. However, I believe you made a typo there and you mean uniblue spy eraser. I doubt that that would get in the way but again I don't know exactly how it works.
So I believe your problem is one of having two resident AVs installed on the same system.