First off, thanks for posting/sending info as requested. Our initial thoughts were that there was something in the Qualcomm chipset that was causing issues. However, the NIC types and driver details were all over the board.
The post from John Gurthy about ESET set off a hunt on that. As Bryon mentioned, uninstalling ESET resolved the problem. However, as the laptop we were using to test was mine, keeping ESET uninstalled wasn't an option :)
I did some digging and I may have found the issue: It looks as though ESET has some issues with their SSL/TLS scanning as there are a lot of posts from people having problems with it and how pages are unresponsive, etc. So I tried a few things. Here's how I was able to fix the problem. Mind you, I'm running ESET Smart Security 9.0.375 with all current updates to the app as well as my virus signatures..
1. In Advanced Setup, Under Web and Email, I turned off "Enable SSL/TLS protocol filtering".
2. I then closed all browsers, then opened up Chrome.
3. I went into chrome://settings/clearBrowserData and cleared out all cookies, Download history, Cached images and files and Hosted app data.
5. I then logged into SmarterMail in Chrome.
6. I then went to our website. (Usually, the page would load but the live chat icon would NOT.)
7. Everything was working just fine.
8. I went back into ESET and turned Enable SSL/TLS protocol filtering back on and repeated steps 4 - 6. Again, all worked just fine.
9. I then repeated steps 4 - 6 in Firefox AND Edge, and they both worked as well.
So, my guess is there was something in an update to ESET in the past week or 2 that borked the SSL filtering.
As mentioned, this was using ESET, but if there are other security suites installed on these computers, they could be causing similar issues. This would explain why uninstalling fixed the problem whereas simply disabling features did not. I hope this helps some folks...