This really belongs in the Corporate Water Cooler, but here's my $0.02 - partly tongue-in-cheek.
It seems like you want to be a BOFH.
I'd take a more sneaky, sorry, less aggressive stance on this if I was in your position:
Basically accept the general idea that, if asked to make the coffee, that is just part of your day-to-day duties.
However, I used to find that if asked too often - and I accidentally gave white instead of black, or 3 sugars instead of none - that people would back off a little. When you get the order wrong 3 times running, people stop asking. Replacing sugar with salt can get them to stop even sooner.
In this case, a wrongly inserted typewriter ribbon or two, coloured paper in the photocopiers, a renamed win.com - or even the odd access denied on various important files on the network - may soon get your users thinking that they could perform some tasks better than you - but none of them would dream of doing your "network stuff".
Always apologise, and say you were in a hurry to do something else extremely important at the time. If you really have made a mistake, don't apologise, but use lengthy technical discussions to illustrate why the issue came about.
Alternatively, do as many menial tasks as you are asked to - and don't have time for the important stuff. That will soon help your users decide where your priorities lie. You may need to be selective here, so that you don't impact users who don't plague you in this manner.
In fact, a few favours done for "useful" people may help you if you need support (and you may do if you follow my advice too closely!).
If they're thinking of putting you on the switchboard, try to have a console close by, or get a friend to text message your mobile phone, so that, if an "important" network duty crops up, you simply have to leave the switchboard to attend to it.
If possible, try to get someone truly incompetant to cover for you while you do this important task. Even better, get someone extremly competant (Although they'll never forgive you if they get re-assigned to the switchboard!).
If people are taking liberties, have a little fun returning the compliment - I certainly wouldn't advise doing any of this in a malicious manner.
In other words, keep within your job description, do everything willingly - but don't let them grind you down! Above all, enjoy what you do.
Good Luck!