Note that many websites have their own advertising, unrelated to adware.
Network Essentials is an IE Browser Helper Object which monitors URLs being viewed in the web browser, and a process which updates the list of targeted sites and downloads and displays pop-up adverts when directed to do so by the BHO.
Please check your system for DownloadWare and remove it before removing Network Essentials. Otherwise it is possible DownloadWare could re-install it, along with much other questionable software.
There is normally a 'NetworkEssentials' or 'MediaLoads Enhanced' entry in Add/Remove Programs that does a good job of removing this; you may also like to delete the registry keys 'Updater' and 'Hopper' or 'MediaLoads Enhanced' in HKEY_CURRENT_USER\Software after the reset to clean up.
Finally there is a 'Digital Signature' HTML file which Network Essentials puts in your Windows directory when it gets installed, which claims you have agreed to some terms and conditions you will never have seen! You can delete this nonsense.
The software installs itself into your Program Files directory. Before you can delete it you must ensure the BHO and task are no longer running.
To get rid of the BHO, open a DOS command prompt window (from Start->Programs->Accessories) and enter the commands (for the NE variant):
regsvr32 /u "C:\Program Files\Network Essentials\v8\ne.dll"
(You may need to use a different number if yours is not 'v8'.) Or, for the ME variant:
regsvr32 /u "C:\Program Files\MediaLoads Enhanced\ME1.DLL"
(You will have to change the above path if your Program Files folder is on a different drive or has a different name.)
Reset the computer and you should be able to delete the Network Essentials folder.