Hi Ingajohn, in answer to your query the short answer would be no alas.
Clearly it does work so the issue is most definitely particular to your machine but tracking that issue would require a full knowledge of everything running on it to see where the difference lies. Could be anywhere, web-cam drivers, web-cam itself, add-ons to browsers, firewall and / or anti-virus, wireless 'V' direct connection and so on.
But if it works on the other machine I'd save myself the headache of troubleshooting and just enjoy it on the working one
Hope is but the first step upon the road to disappointment.