First, good on you for thinking about your resume and employability well ahead of time. You should be able to build a solid resume to job search with by the time you graduate.
Now, let's clear up some terms and misconceptions. A service industry job like the one you did part-time is what you'd call pink-collar work. As a future Computer Science graduate your career will be that of a white-collar office worker. The issue with pink-collar experience is that it simply doesn't translate into office experience because there aren't a lot of transferable skills. It does show that you're employable, meaning that you can be expected to behave professionally and responsibly in the workplace. What it boils down to is that this kind of experience is a great differentiator when you're in a pool of candidates with no work experience but candidates that have white-collar experience will have a strictly better profile than you. Now, because you'd be applying to entry level positions, that shouldn't matter as much because the people applying for those typically also don't have office experience. Sadly, today's job market means that job openings often have a lot of (over)qualified candidates.
That brings me to something else I wanted to correct: hiring managers don't "deny" you a job. They have a responsibility to hire the best person they can find for the job and that means that the only way to get hired is to be that person. There are no tricks and shortcuts, the key differentiators are work experience, cultural/social fit and skill. The way to land interviews where you can showcase these things is by applying for positions that match your resume and writing great cover letters.
In your position, you'll want to apply for any student internships you can get that involve office work. Check with your college for on-campus jobs if you can't find any other leads, but ideally you'll want to find part-time work or a summer job in the private sector. If possible you want that job to be IT-related. Consider your busboy experience your first step into the professional world and use it to land a job or internship closer to your interests and industry. By the time you graduate you should have a few years of part-time work on your resume that will hopefully include office experience and with that you should be in a great position to apply for entry-level IT positions.
Now, for your questions:
1) Can I put down that I have 1 year of work experience?
Yes, but you'd list it as part-time. To do otherwise is tantamount to lying which is a great way to remain unemployed. Unless specified, jobs listed on a resume are expected to be full-time or close to it (3/5, 4/5ths).
2) Can a hiring manager reject me after discovering that I lied on my resume?
Yes, obviously. I'm aware that this isn't what you wrote but that's basically what it comes down to. Don't ever misrepresent yourself on your resume.
3) Should I consider getting an internship as soon as I can?
As I mentioned above, you should apply for internships as soon as possible. Internships come in all shapes and sizes. Your goal should be to try to build professional office experience with your internships or part-time work so that you can land a full-time paid entry-level job the moment you graduate.
