What we do is start a timer at the beginning of test execution, which fires every 5 seconds, to detect if our application (which, in your case, is the browser) has crashed or stopped responding. Check out the TC help files for timers.
Please see the "Using Timers" help topic for more information about the Timer object. Also note that when Internet Explorer crashes, the window stating the crash may appear. TestComplete can handle this window and treat it as an unexpected window. So, you can add the OnUnexpectedWindow event handler to your project and, thus, detect the crash. Please see the "Handling Unexpected Windows" help topic for more information.