Think of the rectifier as sort of a check valve for the generated AC current. The AC current will [on a good rectifier]flow only one way,to the battery,and by the time it goes through the rectifier,it is now DC current.First thing I would check would be for power getting to the rectifyer. If you have power getting there, then the problem would be after.
As Dods stated, you will probably want to check all the wiring over.
I would like to say that it may not be so much as a short as a loss of continuity somewhere. If the connection is not there, then the jiuce cannot get to the battery.
If you can get a hold of a Honda repair manual, there are simple tests that you can use to make sure your rectifier is OK. On the Honda page of this site,right at the top of the page is the link to find the free manuals