I started as a Network Admin in the early 90's. The way I transitioned into programming was to start creating applications that made my job a lot easier.
For example, there was a lot of setup involved in creating a new user. From creating the account, to assigning the appropriate group permissions, to creating the home directories, etc. We had some scripts we ran to handle most of this; so I coded them into a regular windows application and cut down our user provisioning time from an hour to 5 minutes.
Once that happened I had a bit more free time to look in other areas of the company that needed help. This lead to building several other smaller applications. Because we had weekly staff meetings with the IT director, I was able to promote my programming skills and eventually get moved into regular development.
Incidentally, we have a network guy here that has been instrumental in resolving web application issues. He has expressed interest to our IT director about moving into development and has started coding some site management tools. I'm sure he will be a regular developer sometime this year.
Basically you just need to start doing the job. It's much easier to make the move within the same company than it is to just go out and get a developer job with no prior experience.