I think it must be something other then Windows update causing it. Or it could be Windows update is trying to update a Network driver which would indeed drop your connection while it installs. Do you get any notice that a update failed to install? You may try and go to the HP website and download the network driver from there. It could be that their is a issue.
It sounds like a serious software issue and one I couldn't help with over the Internet. I recommend you:
1) backup your entire computer contents (Windows 7 IMAGE to a USB drive)
2) copy e-mail, document files etc to USB drive folder
3) RESTORE the original Windows 7 installation (on your original hard drive; see MANUAL)
4) Updates, drivers, programs etc
You should consider using Acronis True Image (Western Digital version is free under hard drive software; use it to make ANOTHER image, however you can SEARCH this one using Windows Explorer in case you forgot some software)