Damn this kind of problem was prevalent in the DSL 56kbps modem days.

Before you try anything else, cross check this :
https://productforums.google.com/forum/#!topic/chrome/gIfjB3z7V48

You might have blocked downloads. Could be caused by an infected reg file.

Also, the trickling down of download speed to 0 is not the problem, the download just stops it takes a while for the browser to realize this and update it on the UI.