A relatively modest broadband couple with multiple systems accessing it wirelessly at the same time easily explains why you're getting an inadequate connection speed for streaming. If you're close to a Best Buy (which I assume you may be, since you indicated you went there to test the speeds) you could pick up an ethernet cable and that would easily fix the issue :-)
The alternative (if available for the specific site you're streaming from) is to set the player to do the download first; then show the video -- that will work perfectly (since the entire video will be on the laptop ... no streaming necessary while watching).