Get rid of the noise :
If you can make sure to always have the same environment parameters (e.g. distance from the circle, luminosity...), then you could mask your image just after the Canny edge detection, with cvAnd; here is what the mask would look like :
Hough circles detection :
Now, about HoughCircle. First, this function performs its own Canny edge detection. You are doing one too just before the call to HoughCircle. It may have an impact on the shapes of your circles, because of the way Canny works (i.e. intensity gradient on binary image...).
Speaking about the shape of your circles, just below is a close-up of what your "circles" look like; I would have been very impressed if HoughCircle actually did detect all or even just some of those. It can't give anything good in Hough space. Just to make sure, set the last two parameters to 0 (min/max radius), and try to lower the minimum distance between centers. But honestly, I think you need to find another approach to your problem.
[EDIT]
A possible approach would be to perform connected component labeling (e.g. blob detection). As far as I know it is not possible to do this simply with OpenCV alone, you will need something like cvblob, which is a very good OpenCV-based blob library. In particular, you might be interested in cvCentroid(CvBlob *blob)
.
Cheers