Wow, now it's pointing to your Realtek network card. I would like to try the following. Also do you have another machine that can access the internet or is this the only one?
1. Download this to your desktop first. It's the Realtek drivers from Dell's website. Since you won't be able to get on the internet once we do this we'll have these drivers we can simply re-install if needed.
2. Right-click on your Start button and select Network Connections.
3. Find the icon that represents your active connection. It will show Connected underneath it and likely be called Local Area Connection.
4. Right-click on this one and choose disable.
At this point you won't be able to get on the internet. Let's see if your machine crashes when going to sleep while this is disabled. If it does, please provide the analysis on the memory.dmp file again.
Then you can simply reverse the procedure by right-clicking on it and selecting Enable. We won't need to use the file that you downloaded yet but want to keep it as we may need it.