Hello and welcome to the forum.

First do the following...

1. Run a full updated AV scan to rule out any virus...
2. Run a full scan using malwarebytes, free version heres the link

Malwarebytes

If all comes back fine then you can do a sfc scan. Here's how...

System Files - SFC Command

1. Click Start...
2. In the search box type cmd.exe...
3. When the pop up list comes up go to the top and right click cmd.exe and run a administrator...
4. When the command box appears the type sfc /scannow notice ther is a space between the sfc and the forward slash...

Let it run and if any error's are found then run it 3 more times...

After the above try and reset your IE here's how.

Open IE...
Click your alt button...
In the top left corner click tools...
Click internet options...
Click advanced...
Then click the reset button...

Hello

Now delete any system restore points you have because if you try and use them you will infect your system again.

Hi,
Does sound a bit weird doesn't it!
All the above have come out positive, except you got rid of 3 trojans, did you keep a note of which/what they were?
What sort of firewall security is there?
Is it possible this is somehow stopping it working?
What is the makes and model nos. of your systems?
Thank you.

Hello

Try turning off your firewall then try going on the internet.