When I edit in Lightroom (basically the same as Adobe Camera RAW), I apply sharpening to the image, and then during the export I downsize and apply the level of sharpening for the output intent AKA for web @ 72dpi or print on matte paper @ 300dpi. These options probably exist within Elements... how much sharpening were you applying? And which method? Unsharp Mask is a good way of doing it but I'm not familiar with Elements at all - does that command exist?
And as Bob said, adding some contrast to the image with curves might also help to improve the apparent sharpness of the image, but I wouldn't rely on that solely