Different PC, different program versions installed?
There has not been any mentioning of Vista recently.
You might try to install the Flash player, current version, from Adobe's homepage. Then you'd see two Flash instances in Chrome and disable the Pepper Flash.
(Don't know how to update Chrome's Flash)
More than one browser should be possible, alas not two on WGT (I suppose).
Firefox (my browser) uses the general Flash. Only real downside is that it crashes every other day. Restart Flash, works again. It might be annoying in multiplayer games though.