I have done a LOT of helpdesk work over the years.
Griping about the medical stuff aside -
When an email hits the helpdesk, members of our team will often send an immediate reply of "On it!" or "Calling now" to let both the user and the other team members that someone is on it. If we can't get to it immediately, a simple "We are shorthanded at the moment, we will get to you as soon as we are able." Seems to alleviate the griping.
I do my best to both remote and call at the same time (users all over the country, it's kind of neccesary). This avoids any impersonal feelings. If I am on the phone telling them I am going to fix it - I get MANY sighs of relief.
Once all is well, I send a recap email to the user and the helpdesk group so everyone knows what went down, what the solution was and any follow up / instructionals that need to be sent.

A little communication goes a LONG way.