Occasional non-starting

Two times in the past week, my car, a 2010 Hyunday Sonata, has not
started. Turn the key all the way in the ignition and nothing. Soft high
pitched whining sound while the key is fully turned, but nothing else.
Dashboard lights come on and the button on the keys the lock/unlock the
doors works.
I've called to have the car jumped and both times they have hooked the
cables up to my car, stated that my battery has a good charge and the car
has not needed to be jumped. The first time, I tried starting the car 2 times
with the cables attached with no result, third time the guy from the tow
company tried to start the car and it started.
The car ran fine for 3 days, Sunday evening the car didn't start again. Same
deal as the first time the car did not start. This time the guy who came to
jump my car tapped on the starter to attempt to engage it, got behind the
wheel and was able to start the car while tapping on the gas.
Drove the car to my dealer who ran diagnostics on the car, said that a
ground attachment had come loose and they tightened that. They found a
missing lock clip and want to charge me $500 for parts and installation. The
mechanic said that they weren't sure if this would fix my problem or not. The
car has been starting fine while at the mechanics, no issues.

Is this a fair price for the work they want to do and in people's experience, is
this a necessary repair?