I’m a senior, and I took the old SAT back in January and did poorly (a 2080). I retook it this October and improved significantly, raising my score to a 1580 (on the new 1600 scale). Will that 2080 hurt my chances of getting into top schools?
No
Your chances are not great to begin with even if your higher score was your only score. DD was accepted at both Yale/Stanford and we sat through information sessions with admissions. What WOULD hurt you would be if you decided to take these tests another couple of times in an attempt to get a perfect score, trying to improve on an already great score.
You are competitive. So are lots of other applicants.
Best of luck to you.
This will not hurt you, it does not matter because you have a 1580.
It hurts you a little, but should not stop you from applying if the other areas of your application are excellent.