I am married, 26 year old mother of an almost 11 month old and a school nurse. I used IM frequently in high school and college. Let me initially say that I really like the comments I have read already. Especially 2 points contained in them "my daughter, my rule" / "my property (computer/house/phone), my rule" AND privacy (aka trust) is a PRIVILEGE that has to be earned.
LISTEN: Be the parent acknowledge that you hear her complaints by saying something like "I understand you are upset and feel like your life is ruined." This validates that you heard her emotions and words. Be sure to listen to what she says back. Then stick to your guns!!!!!!!!! Don't let her emotional response to you catching her disobedience deter you from protecting her! Increase the punishment for disobeying... use your judgment for how but draw a line and stick to it. In addition consider pre-stating the next punishment for getting back on IM. For example, if you are on IM again while you are grounded from it, you can't go to the (fill in something she has been planning on doing) football game on Friday night.
WHO: Second figure out WHO is on her buddy list, especially who has been in the problematic conversations. You didn't mention if you have determined who she was talking to, one way or the other. Is it Sam from math class, someone who IMed her online, or a friend of a friend. Remember that you don't want to know what the IMing says they are but what your daughter has seen (She should be able to tell you race <it's a visual thing that doesn't usually come up in IM>, gender, and age/grade pretty easily about each of them and maybe where she met them if you don't know... like I met him when I went to the mall with Jill).
RULES: Third, I would suggest you create an online etiquette that clearly show your expectations for your daughter. (This would be the HOW to type/talk.) Be sure that your daughter understands that the same rule apply to IM, email, chat rooms (I really suggest forbidding those completely since identity of whom you talk to is virtually unverifiable), online multi-player games, etc. Also, I would hope this would be along the same lines of the face-to-face etiquette you taught her since she was a baby.
1) The first rule should be never type anything you wouldn't say to the persons face (or maybe even with your mom in the room). Of note: "Our daughter says we are "ruining her life" by getting into her IM world." Kids today tend to view the internet as a place to be/say/do things they might never get to be/do in reality. The reality is the computer at your office is NEVER private from your supervisors and your home computer and online activity can be used by the courts.
2)The second but very important rule that your daughter can't IM anyone your daughter hasn't met in person. There are 2 ways to chat with people you have never met... 1)Friend of a friends are dangerous, although they sound interesting. The known classmate could have accepted some claimed identity but it could really be a 40 year old pervert. Or the less extreem version is her older 7th grade friend introduces her to her older 9th grade friend. The other way people "meet" online is by looking thorough a directory. One thing many people don't realize is when you first select an email or IM name there is an option to have it listed in an online directoy. This seems like a good way for long lost friends to find your new ID. NOTICE that these directories can be browsed by ANYONE!!!! Don't let her be listed in these directories.
FOLLOW UP:If you haven't already, set a date for re-evaluation of the privilege of IM. "Your father and I will discuss how you are doing in a month/2 weeks and decide if you have earned the privilege back" Then start with a limit on the length of time and time of day she can be on to when you are in the HOUSE, the same room is even better. I wouldn't remove those notifications at all but at least not until she has proven consistently she can be trusted for months and months. An easy way to monitor usage but not specific content is to get an IM name yourself and be signed in on it all the time on another computer (if you have one), then have her (and maybe some of your friends kids) as your buddy. You can set IM to notify you every time when she becomes active or signs in. This only works if you are on IM at the time. You can check "idle time." to tell if she has really just been signed on and not talking or closing the window when you walk up behind her.
I personally had parents who had very clear guidelines for my behavior. They never typed them up but they also were the same since I was a little girl. When I got onto the internet, they carried over. My parents knew that as a kid sometimes it is hard to know what you believe about cussing or whatever the issue is. I was given permission (multiple times) to blame mom and dad. If I couldn't figure out how to tell my friend I didn't want to be IM-ed about her make-out details I could blame my parents. This also held true for ANY activity or party I didn't want to go to, regardless of the reason. They said it was their JOB to be the heavy. Their only stipulation, was that I tell them when I used them as an excuse, so they could back me up and be the heavy. You may want to consider giving her this option to blame you if a friend uses a bad word or starts a ifffy subject. "Remember my mom will read this" or "I really want to be able to IM and my mom is such a pain, and will take it away if we IM about that"
When I got to college a friend introduced me to yahoo games like pool and poker. I often had to be VERY clear that I didn't want to talk about sex, what I was wearing, ect to get to JUST PLAY A GAME. I eventually stopped playing unless I could arrange to meet a friend in the game area.
Best of luck... you are just starting. Be firm... it's easier to loosen up.