Right now I am trying to apply for a part time job at my university working at a desk in a computer lab. I am currently a major in computers and information technology. However the only previous job that I still have contact with an employer for was for a job as a summer camp counselor for teens with special needs. I had that job when I was in my teens and I have not seen that person in years. I know this is not relevant to the job I am applying for but would that employer still be a good reference to use?
So long as the reference is able to talk about attributes that you demonstrated at the prior job that are relevant to the new job, it would still be a good reference.
For example, your supervisor from summer camp can talk about your punctuality, your interpersonal skills, your creative problem solving, your drive, and other "soft" skills that are potentially important for the position you're applying for. Since you're still in contact with this person, it would generally be useful to let them know that you're applying for a job where you've listed them as a reference and to tell the reference what sorts of skills you would like them to highlight. Your reference will generally provide a more helpful reference if you can prime them by connecting the dots of the experience they're familiar with to the skills the new employer is looking for. If the people running the computer lab emphasize the need to work effectively with difficult/ panic-stricken users (i.e. "Can you write my C program for me?" or "Ahhhh, the paper I've been working on for the past 12 hours is gone, my life is over!"), it would be helpful if you have primed your reference to recall how you were able to manage demanding parents and frightened kids. Otherwise, the sorts of things your reference emphasizes may not be the sorts of things that the new employer cares about.
Ideally, of course, you would have a reference that can speak both to these "soft" skills and the "hard" IT skills you would need for the position. But it's likely to be pretty common for this to be the first job many students have, or at least the first IT-related job they have, so this is likely to be a relatively common problem. It's unlikely to be much, if an, of a disadvantage for you.
Of course, that assumes that the university even bothers to contact your references. My wager is that most won't bother.
It depends on whether you are looking for a 'character' reference or a 'knowledge & skills' reference as to which aspects you would like them to speak to.
A non-technical subject related employer can be a good 'character' reference is they can speak to your honesty, work-ethic, commitment, focus, working with others, persistence, timeliness, etc. Indeed some employers (those with more experience usually) may actually rate this stuff higher if they go by the "anyone can write code, but many can't work with others" principle.
If your primary concerns are to have a reference to speak about your knowledge and skills in your given field, e.g. your mastery of languages, how you have solved various logic problems, what solutions you have found to complex technical issues and the details of why and how you created those solutions, then you'll need someone who can do just that.
Many folks try to do both, e.g. 2-3 technical references and 1-2 personal references. Of course if you simply don't have a technical reference then you will want to go with character reference. You can be more creative in creating your 'technical' reference, some options are: work on an open-source project; do some volunteer work; do projects with friends. All of these can lead to a technical reference - even if it's not from the traditional 'employee' one.
Finally, never forget that there can be unanticipated things. For example, you might just meet with a manager who has a teen with a special need, if so your non-related work (and reference) will still carry a lot of weight.