"I have been trying to get an internship and the process has baffled me. People with contacts in big companies have an unfair advantage even though they are not that skilled. No process of hiring is completely fair. Every organization has its own recruitment process. People with contacts in big companies do have advantages but I don't think that's unfair. They have devoted their time networking with employees of big companies.
Even though there are some people who get internships with contacts, let me tell you this: No big company will hire someone for the sole reason that they are recommended. In case of jobs, the contacts can only take you up to the interview table, you have to prove yourself there. There might be some exceptions where the recommendations work, but it is not significant in proportion.
Don't let that feeling depress you, and stop you from trying. Remember, getting an internship is not the only thing that matters. Those who get from recommendation and without talent would eventually find it too tough to bear, and would eventually drop off. You can always get good internships, if you have a good enough profile, interesting skills and good commitment. If you didn't get an internship somewhere, it means something else, something better is waiting for you.