The saying is that pilot's earn their larger-than-bus-driver wage not when things are going fine, but when things go wrong. Personally I would be professionally ashamed to ask for ATC help to navigate my aircraft, when no Navigation equipment on the aircraft had failed - just the box that did the navigation thinking.
And at the subsequent board of enquiry when the aircraft is laying in flames and the court says "Mr Pilot, why is the aircraft laying in flames?" and you can reply " I was ashamed to ask ATC for help when my navigational box failed, I know there is an X million pound radar system down there and I know I was wrong in my calculations but at least I tried"
Personally I'd get as much help as possible!!
