I would look at permissions and make sure that the app pool its running under has write permissions to the folders. Just a thought. My personal preference is create a folder somewhere and give everything full permissions to it, and set a path in the nlog.config file to point to that folder.
<target name="logfile" xsi:type="File" fileName="LogFile.txt" />
Would become this
<target name="logfile" xsi:type="File" fileName="c:\logfiles\LogFile.txt" />
Just to reenforce what studlyed said above - make sure the account your website (app pool) is running under has the permissions required to the logging directory you are specifying. If it doesn't have the permissions - a log file can't be generated.
Buona sera Luigi--
Did you try what was recommended above replacing the "\" chars in the file path with the "/" chars?
If you tried that, and you've set permissions on the target directories, my recommendation would be to create a small test exe that uses the same NLog.config file and attempts to recreate the code path as much as possible. Run it on the same server running your ASP code.
If it works, then most likely there is a permissions issue. Check the identity under which your app pool is running, and specifically set permissions on the target directory for that user.
Finally, you can set the throwExceptions="true" attribute on the nlog element in the config file to see if there is an actual exception occurring that might be causing the problem.
Please post back any problems or findings.