It all depends on what your IT department is set up like. Are your networking / server people working hand in hand with you? System Engineers (the server sysadds at my job) work hand in hand with the Service desk. If you are qualified, can show experience, and have a well written resume.. they will look at you when a position opens up. Same with the networking engineers.
I was in your position back in Dec. I asked the IT manager if they were looking for people and on what teams. He replied that they were looking for NE's to work a hell shift (12's, 4 on , 4 off, nights). I got my resume together, started brushing up on my networking and interviewed for the job. I have a co worker who is in the same situation and they won't look at him. He is trying to get to the systems side of the house. He is a MCSE for 2k3 and can't even get an interview.....
There has to be an opening you can move into. Start working towards your trade certs (juniper, cisco, microsoft, etc.). It will be easier to get to an interview if you have the certs to back it up. You already have your foot in the door. IF you are good at what you do, management will have noticed. They are the ones to talk to about moving up into an open slot. If your companies turn over rate involves death... then you might want to put out a resume.
TIPS on your resume..
1. Proof read.
2. Tailor it to each job you are applying for.
3. Write a separate and distinct objective statement and cover letter for each application.
4. No huge blocks of texts. Make it easy on the eyes.
5. Take the skills listed in the job listing and make sure those words match in your resume, most HR departments do a key word search because they don't understand a tech resume.
6. Give a specific outline for your repsonibilites for each job... if they want to know more they will ask you in the interview.
Once you get to the interview.. the job is yours to lose.. not yours to gain.