Basically, my Mum's laptop had Avast! Free on it, and I un-installed it (as it said it had expired) to install AVG ... And lost all internet connectivity.
After a lot of playing about and surfing the net on my desktop, I found that there are a LOT of complaints online from people who have uninstalled Avast! Free, or even just downgraded from a paid version to the free version - to find their internet connection is blocked.
When I say blocked, I mean it - wireless, wired, and even a USB tethered connection via my mobile were all blocked (though it doesn't say it's blocked, it says "limited or no connectivity" or "no network available"). I tried the same method on my desktop, and there's no problem with the network in each method.
There are numerous "fixes" online ... none of which have worked, so I'm now busy doing a wipe and full re-install of the OS (it needs a spring clean - hasn't had one for 3 years and is getting a bit slow).
So beware of Avast - it works great while you're using it, but has a nasty trick up it's sleeve if you try and remove it!