Problem solving is a huge part of software development and that's a great transferrable skill. Problem solving is useful pretty much everwhere. Definitely emphasize how you were able to take an intimidating, complicated task and break it down into manageable pieces.
Communication is another great transferrable skill - it's so easy to build the wrong thing if you don't fully understand the requirements. If you did any requirements gathering or communicated status to other teams that's going to apply to just about any job. I think requirements gathering would be an especially good skill for a student advisor - if the student knew exactly what they needed, they probably wouldn't need an advisor :)
Attention to detail is a good one too. I've never been an admin but I bet they have to keep track of a lot of fiddly little details. Software development just doesn't work at all if you don't implement the exact API you were asked to.
Ability to learn on your own - another thing that's useful anywhere. Being able to google stuff and figure things out on your own instead of sitting there waiting for someone to walk you through it is always useful.
Computer skills - general stuff like being comfortable figuring out how to use a new application or to learn advanced features of something everyone uses like a word processor or spreadsheet program.
Software development itself can be a transferrable skill if you're willing to do a little bit of it now and then. There could be some tedious task or part of a task that you could automate with a quick script and being able to do that could make you a huge asset as an admin.