As a helpdesk analyst, I would say understanding the client and understanding the issue lead to the most important skill that is required. Provide a viable solution. This does not have to be "the final solution" but it does have to satisfy the customer's current needs and lead towards resolving the issue completely.
The customer does not want to hear excuses; they do not want to hear about problems. They want to hear that the issue will be fixed and when it will be fixed. If you can not resolve the issue right away, then setting a time for when you will update the client will almost always walk away satisfied because their problem was taken seriously.
I also find being able to remain quiet an excellent skill. Sounds easy, but it is rare to find a customer support person who will not interuppt you. I see it on my desk all the time, people who cut off the client because they have to solution already. Just waiting that extra 30 seconds for the client to finish goes a long ways.
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