After I typed up all of the following post, I realized that every bit of this is assuming you're using U.S.A. copyright law. I'll let you make sure that this is the case.
Most of what BarabiSama said holds true and is good advice. I assume that when you say an Abridged series, you mean a series of abridged, re-dubbed clips from Drrr with a comedic purpose. (Yes, it has to be for comedy.) In this case, you're allowed fairly extensive use of the original work's material to properly imitate the original. HOWEVER, your parody must not interfere with the original work's ability to generate revenue. The idea that making money off of something doesn't make it fair use or not making making money makes it fair use is completely false. As long as your production and advertisement does not interfere with Drrr's ability to make money, copyright law doesn't care if you make money. (Now I would not try and stretch this if I were you. You're generally better off not trying to monetize this since it's just a fan work.)
The bit BarabiSama said about the music (the OP, the background music, and possibly the SFX) is very important. Music production companies are much more aggressive when it comes to stuff like this than anime studios. If you want your series to have music, use music that has already explicitly been marked available for reproduction. Orrrrr, it would be way cool if you contacted some of the many artists on YouTube that do anime cover songs and get one (or more) of them to do your music. I think that would be a fun way to add some legitimacy to your product, spread your potential audience and fanbase, and increase the quality of your product all while adhering to copyright law.
Now even if you do break copyright law at some point, you'll probably be fine. Just about every abridged series I've watched has had some sort of breach of copyright law somewhere, and most of these series are one egregious breach of the law. Don't be lazy, do your homework, and try to involve the entire community. Good luck!!
>>16 If you admit to not having enough knowledge of copyright law or the American legal system to contribute helpful knowledge to the project, why did you spout misinformed bullshit with your "low hopes?"