It sounds like your school is using that software to enforce a no NAT device policy. Is there some particular reason you need to have a router? You can't just plug in a switch (or use the router as a switch) to share the single wall jack with multiple computers in your room?
yoji :
P.S. while you chatting to your school.. ask them to teach you about double negatives...you seem to have missed that class
Double-negatives (or triple- or multiple-negatives) are used in certain parts of the U.S. (mainly the South) and in some other countries as a form of emphasis, not a double negation. "Without no problems" is just a way to say "Absolutely no problems".
Negation itself in proper English is sometimes logically incorrect. If I ask you, "Haven't you finished your homework yet?" In English, a "No" is an implied self-referential no meaning "No, (I have not)." It makes sense if you reply "No, I have not." But doesn't make sense when you answer with just "No" - the self-reference is ambiguous. Is it referring to "No, (I have not)" or "No, (contrary to what you are asking, I've already done it)"?
Asian languages avoid this problem by just answering the question that was asked. "Yes" = "Yes, (I have not finished my homework yet)". "No" = "No, (contrary to your question I have already finished my homework.)" No ambiguous implied self-reference.
After a while, you learn all these little nuances of language as different people use it. Not assume it's a flaw in their intelligence or education.