Based on what I've heard, Chrome is not very flash friendly. If the survey is using flash, it could be the Chrome buffer overloads and forces a shut down. Typically I would only expect the browser to crash, not the whole PC.
First, I'd suggest ensuring you have the latest Flash plug-in installed by going to adobe.com, then I would check if you have the latest Java installed by going to Java.com. That should rule out any usual suspects from a software perspective.
I typically use Firefox browser and have done video surveys like you've described and have not had any issues with them using that browser. You might want to try using a different browser and see if you can get through those surveys without the crash. If so, maybe it's a Chrome issue?
If the same thing happens with a different browser, then it seems like some driver or hardware might be failing (like maybe a video driver). To ensure your drivers are up-to-date, a tool I use is SlimDrivers application - I use the free version. Once installed, run it and the tool will see if there are any pieces of hardware that are out of date and let you update the drivers it locates. If you use this tool, if you get a large list of updates needed, I suggest slowly installing them - install a couple one day, wait a few days, install a few more. Sometimes if you install too many things at once, that can cause it's own problems.
The last thing, if it's still crashes, is after the crash and you reboot, click the Start button. In the "search for program" text box type in "event viewer". Open the application once the search finds it. Once the application opens (give it a couple minutes to open and display the list of items), in the left navigation tree, open "Windows Logs", the click "Application". In the list that shows up, scroll down until you see a red exclamation icon around the time of the crash. That is probably the application that erred causing the crash. Clicking on that line will provide information on what was causing the error in case you need to call for extra help. If you don't see any red exclamation icons, try selecting the "System" option and look for any there - those would be hardware issues.
What I do if I find an issue in the logs is search on the error and application to find forums where others have had that problem to see if there are any documented solutions to try. If you're not adventurous enough to try that, at least you'll have information when you call a help desk for support.
Hopefully your issue will be fixed before having to dig into log files.
Good luck!