There is an identd option is mirc 'enable only when connecting', make sure this is turned on, then you can rule out mirc causing a problem. 
 
A few other common issues are certain software firewalls or anti virus type programs that can by default block identd requests.  Another common issues is router settings, there are a number of routers with an option (enabled by default) that blocks requests on port 113.
		 
		
		
		
		
		
		
		
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