DISCLAIMER: I have never had an internship and I'm not an accountant or an auditor. However, I've always been able to find work when I needed it, and over the years I have worked in computer consulting, I've worked with and socialized with employees from Accenture, PWC, Deloitte, KPMG and many other smaller companies. If I were attempting to get an internship at one of these larger places, I would try several different methods:
1) Use information gathered through a work-related social network (probably LinkedIn but you may know of others) to learn about (first) and establish some communication with (second) people already working there. Use caution as always when contacting strangers, and try to communicate with them in a structured way during usual business hours.
2) Reach out to accountants/auditors or other professionals through businesses in your area to try to establish an indirect connection with someone who is working with one of the firms where you want to get an internship. These folks are probably going to be very busy because smaller businesses have fewer resources, so be respectful of their time. You might even offer to do some short-term volunteer work for them to let them know you are serious if the place seems interesting to you.
3) Find out where the nearest regional office is and walk in the door to find someone who works there and ask them some questions. If you can find someone besides security and they're willing to help you, then that's great, but don't expect too much here. This is just a step you can take to get used to the situation. There may be other visitors if it is a busy office, and you might meet others who are waiting to be let into the building for a meeting. Asking for help or information might generate another contact.
4) Establish connections with employees by attending social or professional events in or near your area. I'd lean more toward the professional events which may turn into social events afterwards, but everyone is different, and my recommended approach may be different from yours.
Some of these things will be easier than others and can be done anywhere using your phone or a laptop like 1) and 2), while others might require more preparation, and I guess the sequence I have shown above is how I'd recommend going about the search. That's because you'll get some practice as you begin this work, and you'll want to get some of that learning out of the way before you get in front of the people who will decide whether or not you'll get an internship. Also, you will get information that will help you learn about the kinds of people you'll meet in steps 3) or 4) and you'll be better prepared when you get those meetings.
One of the things I remember about a college roommate I had who had pledged a business fraternity and who later worked for one of the big-six (back then there were six) was how important phone etiquette and politeness were when arranging or attempting to arrange the many meetings he needed to get into his chosen fraternity. Just as important as the professional tone was the persistence that he showed in the face of a ridiculous number of rejections as he attempted to setup meetings and get someone to sponsor him. This difficult learning process must have played a huge part in his later efforts to become part of the firm where he eventually landed after school.
Keep in mind as you reach out to people that they will probably be more busy on Mondays. They may be out of the office toward the end of the week, and they probably will be tired at the end of the day. Also, you might want to wait until after they have had their morning coffee before you make your introduction or contact them for assistance. By mid-morning on Tuesday, they'll have had enough coffee and hopefully will be in a good enough mood to be open to helping someone new.
Good luck and be careful. Also, keep your eyes open for opportunities along the way to your ultimate goal of a big-4 internship. You might find that you are more comfortable at one of the smaller firms, and if you are just starting out, you will probably also find that you'll get more experience sooner at a small firm if you do choose to go that route. On the other hand you might find that larger organizations suit you best and provide more opportunities for advancing your career. An internship is probably a really good way to find that out.