This is from my own personal experience, so there's obviously no guarantee you will have the same experience, but I thought I would share...
I also had some difficulties with abuse during my undergraduate years, my grades suffered and I ended up withdrawing completely from the course, eventually completing my BA 7 years later from a different university. I'm now completing my PhD at one of the top universities in the US, and before this I did a masters at one of the top universities in the UK. So it certainly doesn't have to hold you back.
In my case, I chose to do a few things to try and maximize my chances of getting into the school and program I wanted:
1) I chose to do an masters before applying for the PhD - to show that I could do graduate level work, and, perhaps more importantly, that my grades really were back on track (that is, that the bad grades were the exception, not the good grades).
2) I referred explicitly to the problem years in my personal statement.I briefly explained why the drop in grades and eventual withdrawal occurred, but really focused on the fact that it was now resolved, and highlighted the consistently positive grades etc since.
3) I asked one of my referees (who knew what had happened), to directly address it in her letter of recommendation, again focusing primarily on the positive steps/grades etc since.
For me this worked really well. I was offered a place at each of the graduate schools I applied to, and although it may have taken me a little longer to get here than friends who didn't have similar problems during undergrad, I'm now exactly where I want to be, and couldn't be happier.
I hope this helps in some way, and good luck!