I'm aware that my time in is worth something, as I did obtain rank that probably looks decent, but I'm slightly edgy as to how it will be received. (I was an infantry Sgt.) Some have some derogatory views of how we are and I'm reticent to mention too much. (Everyone thinks you have PTSD despite studies)
It is important to get in with the right company though as many helpdesks are basically outsourced to the lowest bidder and end up being dead end script reading jobs (done those myself, do not recommend).
One company that might be worth looking at would be Rackspace (they host the website for the British Army so I would assume they are not anti-military) they are also a pretty large and growing company.
Another option would be to work with a small web dev shop. Usually they are not looking for uber-coders but for people who can produce consistent work on time. Also Linux knowledge (if you also know your way around Apache) tends to be very useful to these guys as they may be so small that they don't have a full time sysadmin on staff and are constantly being frustrated by the slow response times of their hosting providers support staff.