Ouyang, I think it's all about the visa. Visa laws stipulate you cannot live on one school's visa while studying at another school. It seems your new school did not carry out their responsibility of explaining the law and appropriately handling your visa. I don't know why they asked you to get proof of transfer but then didn't follow through by giving you a new visa. It's their responsibility to know what visa you are on and how you are studying at their school.
Since you used KCEL's visa for an entire semester, I think you're left with no choice. If I understand correctly, since you lived on the visa, you end up having to pay for the semester. The money is related to the visa as much as it is to your participating in classes, simply because of the strictness of the visa laws. If I'm right, to do otherwise is illegal.