The idea behind the driver installation order is installing Intel® WiDi software at the end as the other drivers are required first; however, you already have Intel® WiDi installed so, this is not the same issue.
I tried to reinstall all concerning drivers. I've removed Eset Smart Security, unistalled WiDi application and PROSet Wireless then rebooted. I've installed latest driver of HD4000, PROSet ver 6.1.3 and WiDi application 4.2.19. Still doesn't work. LG TV is visible for WiDi application (signal strength on your graphical indicator is point and two lines, TV set is 2m away from notebook) but during connecting it tries to find a device (probably TV) and it finds nothing.
The Application Event Log contains following record that appears during such unsuccessful connection.
-<Event xmlns="http://schemas.microsoft.com/win/2004/08/events/event">
-<System>
<Provider Name="Microsoft-Windows-ApplicationExperienceInfrastructure" Guid="{5EC13D8E-4B3F-422E-A7E7-3121A1D90C7A}" />
<EventID>1</EventID>
<Version>0</Version>
<Level>3</Level>
<Task>0</Task>
<Opcode>2</Opcode>
<Keywords>0x8000000000000000</Keywords>
<TimeCreated SystemTime="2013-09-05T15:28:43.309222300Z" />
<EventRecordID>32418</EventRecordID>
<Correlation />
<Execution ProcessID="6720" ThreadID="6724" />
<Channel>Application</Channel>
<Computer>HabanR-NTB</Computer>
<Security UserID="S-1-5-21-XXXXXXXX-YYYYYYYYY-ZZZZZZZZZZZ-1006" />
</System>
-<EventData>
<Data Name="DBType">15</Data>
<Data Name="AppNameCount">30</Data>
<Data Name="AppName">Intel Wireless Display (WiDi)</Data>
<Data Name="VendorNameCount">6</Data>
<Data Name="VendorName">Intel</Data>
<Data Name="SummaryCount">99</Data>
<Data Name="Summary">To function properly, Intel Wireless Display (WiDi) must be reinstalled after you upgrade Windows.</Data>
<Data Name="SessionID">1</Data>
</EventData>
</Event>
What else could be reinstalled?