I am not a theologian, so take what I say with a huge pile of salt, but I was in your position and reasoned as follows:
Piracy in and of itself is not theft – even the medieval monks regularly "pirated" texts by copying them down without the permission of the original author.
However, modern internet piracy is an inherently disordered act for two reasons:
1) You must disobey the law of the land to do it (and there is no proportionately grave reason to require disobedience – it's one thing to disobey if the government forbids you from saying mass or forces you to abort babies, but it's another to disobey so that you can watch your favorite films for free)
2) You must violate the contract you signed with your ISP and force them to use their bandwidth for something they do not wish it to be used for, causing them to commit a crime in the process. In other words, you not only violate a perfectly reasonable contract that you entered into in good faith, but you also cause the company to become an unwilling accessory to your sin.
Just my 2 cents. Consult your priest/spiritual director, obviously.