Ignoring the joke answers this is probably the best answer here.
We work in support services - unless you are an IT service provider you aren't part of the business that makes money. You support the business, but you aren't the business. Think about all those other support functions, HR, finance, legal, office facilities - they are all needed too but I don't often hear them asking to be appreciated by management.
To the OP - What is your objective? You say you want management to "appreciate the hard work that an IT department does?" - but why?
* Job security?
* To make yourself feel good?
Turn the question around and ask "What does management appreciate?" - Face it, you aren't going to change your your boss but you can change the way you communicate, or better still, change the way you do things.
Do they value cost control? Show how you did your job on a budget - grab some analyst papers and show how you do it cheaper then comparable industry segments. If you start reporting on this then it will also drive yourself to manage costs well, so you should be able to report on cost savings and improvements. Be honest about who YOUR competitors are - your should be benchmarking yourself against outsourcers and "cloud" vendors. Again, this drive behaviour, make the cost comparison and deliver what management really wants.
If you have management that hates downtime, but you have trouble showing the hard work you do to maintain that - rethink what you are doing. You aren't keeping the systems up, you are addressing things that could go wrong. Do you maintain an operational risk matrix? Start formally recording and tracking what could go wrong, use it to focus you work appropriately and summarise this to management to demonstrate all the monsters under the bed you are chasing out that they never see. It is also a great way to get funding if you report on something in the risk matrix for 18 month as a future issue.. You have the opportunity to forecast things like hardware refreshes and forced software upgrades to management - presented in terms that are meaningful to them (e.g. "medium risks of downtime costing >$250,000 revenue can be resolved for $75,000") and you are able to report on all the risks you have removed? Are you working on things that aren't in the risk matrix? Why? Either get it on the risk matrix, start reporting it as project work (that someone else can justify the value of) or stop doing it.
Excuse the cynicism, but while it is possible that you are doing a great job you management would love if they knew, the fact you are asking the question highlights that you don't understand what senior management values. If you don't understand, how do you know you really are doing a valuable job? Sure you are working hard, but that isn't the same. I have seen technically competent hardworking people loose their jobs to outsourcers because they weren't delivering what senior management expected. Unless you are prepared to re-think your priorities to you are not going to get the results you want.