Hi Julian,
Thank you for posting your query in Microsoft Community forums.
I understand that you are unable to get an error message while downloading google chrome.
Before we try fixing the issue, I would suggest you to answer the questions given below.
1) Are you using Internet Explorer to download Chrome and Google Hangout?
2) Do you have any third party security software installed on your computer?
If you have any third party security software installed I would suggest you to disable it and check if the issue persists.
Disable third-party Security Software
a) On your Computer screen Task Bar next to System Clock..
b) You will see the third-party Security Software Icon.
c) Click on the third-party Security Software Icon, you will see a pop up.
d) In that pop and select the option to disable, click on it.
Now the third-party Security Software will be disabled.
Important Note: Antivirus software can help protect your computer against viruses and other security threats. In most cases, you shouldn't disable your antivirus software. If you have to temporarily disable it to install other software, you should re-enable it as soon as you're done. If you're connected to the Internet or a network while your antivirus software is disabled, your computer is vulnerable to attacks.
If the issue still persists, I would suggest you to contact Google support regarding this.
http://support.google.com/?hl=en
Hope the information helps, if you have any further queries, feel free to post. We will be glad to assist you.