First, I would check the zone security settings on the Internet Options -> Security tab. Default settings should work fine, if any except the Restricted Site zone are set to "high", I would decrease those to "medium" or reset to default alltogether via the dedicated button.
Add-ons you can check by opening IE, clicking on the settings icon in the right corner and selecting "Manage add-ons". I would temporarily disable anything in the "Toolbars and Extensions" category for testing purposes.
If neither of those things make any difference, I would then go to the "Advanced" tab in Internet Options, and restore the advanced settings or, as a last resort, reset IE to its default settings altogether. Both can be done from the "Advanced" tab.
Inquisit makes use of IE under Windows to render HTML because IE is present on every Windows system, other browsers are not. It does not matter which other browser you may use to browse the web or that you've set some other browser as your default browser, those browsers' settings have no effect on the HTML rendering in Inquisit.