No internet function for applications, but nw says "connected"

I wasn't sure what subforum would fit. Browser and email are involved, but broader than that. Probably not hardware, but at this point who knows?

This is long description. Bear with me.

Configuration: Hardware. Two computers connected to router which is connected to Dishnet satellite modem. No local network or homegroup set up. Both machines running Windows 7 sp1 with all updates. The computer I am typing on works fine with full internet functionality. From it I can log onto the router and the modem. Neither indicates a problem. Router shows both computers connected.

On the other computer, which is my wife's computer:

Windows control panel/network&sharing shows network connected with internet access. From cmd prompt I can ping, pathping or traceroute to WAN sites, e.g CNN, amazon, xkcd. Ipconfig shows nothing obviously wrong.

Firefox opens but immediately gives server not found screen for any url, including the router and modem dns addresses. Internet explorer will not successfully open at all. IE window appears but then says not responding, then closes after a minute or so with no further message. Avast (free version) shows warning that one shield is turned off, but does not respond when I select the turn on button. If I open Avast user interface it indicates no internet connection. The Avast warning is odd in that all three shields (file, mail, web) indicate as running. So what is the one that needs to be turned on?

Just before this started, I downloaded a large windows update (appx 25 items for Windows and Office), avast program update to new 2015 version, several adobe updates, flash, java. For some I used the Avast software update utility and some used application updater. All seemed to work. Still had internet function at that point.

Then I tried to find and uninstall the mdnsresponder version of Bonjour (I know what it is) because avast had popped up warning about it (rootkit I think) for past couple days, starting before I ran all the updates. Each time checked "delete (recommended)" from avast warning choices.

I found that the bonjour service (with cryptic numerical name) was already disabled, which I did a couple years ago. Any uninstaller was hidden, so I tried some manual uninstalling. My fooling with it was close to the time that internet connection failed, but I didn't notice exactly when, because the indicator in the taskbar showed, and still shows, connected. I also opened the Avast firewall setup page but didn't do anything, because it appears to be available only in the not-free version.

Eventually I tried to look something up on internet and found the problem.

Turning windows firewall and avast shields off does not fix the problem. Comparing settings between the two computers shows nothing obvious. The good one doesn't even have bonjour or dnsresponder.exe on it.

I have done all I can think of over several hours, except attempt using a restore point, because the last one was before the windows update. With so many changes, I am skeptical that it would succeed in restoring everything. None of the changes made after the windows update appear in affected programs list. Only the windows update items. One of those other changes would be the source of the problem. I'm nervous about making it worse with a failed restore.

Before I make an image of the current state, then try restore point I was hoping this half on half off internet connection would sound familiar to someone, who could aim me in the right direction.