Improving reliability improves the user experience for all of your employees. The best way to improve reliability is to standardize processes, procedures, and applications as much as possible.
Tracking down the root cause of an issue so that it can be fixed permanently and quickly will make your employees (your internal customers) more satisfied with IT's work. This has two effects: internal customers recognize that problems will occur from time to time, but their main concern is how IT reacts to it and fixes it.
Is there a regular process in place to diagnose the problem, solve it, and document the fix? By doing this, others who have the same problem get fixed very quickly and new workstations that are rolled out can have the fix pre-installed. This is the foundation for ITIL - Information Technology Infrastructure Library. Identify problems, determine root causes, create solutions, and share the information widely so the process is smoother the next time.
Be warned, however, that things will get tougher before they get easier. Documenting and going through a standardized process takes longer initially, but subsequent repairs and fixes take less time because the fix is fully documented.
Gather information from the Help Desk statistics and determine what the most common issues are. Figure out what the root cause is and then develop a standard solution for it. Going forward, that issue should be easier to fix and may even be eliminated if a permanent solution can be found. What actions or processes have changed as a result of your Help Desk ticket analysis?