I am in computer networking (worked for a telecom equipment manufacturer for 10 years). I have been intrigued by the idea of working for the church for a long time and watched for an opportunity to come up, but the Church has not (yet?) posted anything that I thought was a good fit. However, I can say that there are jobs to be had for those in computer networking. If you are coming out of a degree program with excellent grades (and possibly willing to relocate - depending on where you live), I would be really surprised to learn that you couldn't find a job - even in today's economy.
Your school should have a job placement program that can help you find a job. This is the place that companies come to hire new grads. And I would suspect that you could leverage your maturity and stability when compared to the typical new grad. Also, as lajackson mentioned, your ward employment specialist may be able to help and allow you to build on what people already know about you.
Good luck, and don't forget to lean on the Lord to guide and help you. He is there, and He cares!