I don't quite understand what you mean by a "special power of attorney."
A power of attorney authorizes someone else to take legal actions on your behalf. If you are asking whether you can give power of attorney to a non-lawyer and have them represent you in court, the answer is "no."
You can represent yourself in almost any legal matter if you can't afford a lawyer or don't want to hire one, and a power of attorney is not required. However, only lawyers are allowed to represent other people.