Office 2013, click icon nothing happens, no errors, no eventlog, MANY clients with this issue

Question

We're an IT solutions provider for companies of all sizes as well, as residential users, and we've been plagued by a new Microsoft-caused issue that's seriously affecting our client's perception of us since it seems like 'you didn't fix it the first
time' or 'you sold us the computer', so it's our responsibility to fix for free.
We've experienced this with 17 people so far, ranging from residential clients with systems that have come from big box stores and from systems we've sold with Microsoft Office 2013 and basically the entire suite stops working.
If you click an icon, you may see an hour glass for a few seconds and nothing happens (but usually nothing happens at all, as though you didn't click it).
Diagnostic steps:
No errors in eventlog, neither under system or application.
No third party add-ins, sometimes it's a stock install on a new / fresh system.
Starting Microsoft Office applications in safe mode, like winword /safe, has no effect.
A quick repair or an online repair will not resolve the issue, it will say it's done but issue still exists.
Microsoft Office 2013 cannot be uninstalled, we always receive the same error code: 0-4
Some systems do not have third party antivirus, some are simply using Microsoft Security Essentials.
This affects all Microsoft Office applications, including Outlook.
Makes no difference if you use another user account or run-as admin.
All Microsoft Office 2013 updates have been installed.
The installation source is undetermined but recent issues stemmed from a physical media (.ISO) install from Microsoft's latest source.
You cannot start the software by clicking on documents created with Office applications.
The only way to remove Microsoft Office 2013 is with the removal tool "O15CTRRemove.diagcab".
The problem returns after a random period of days and no client can relay the actual cause of the issue, it seems random in nature. After the issue is experienced, we go through the same steps including the necessity to utilize the removal tool.  
This seems to be a new issue that's come out of the blue within the past few weeks, at least on our end. When 17 random people call out of the blue with the same problem, it suggests it's Windows Update related.
I'm really hoping someone has some insight into this Microsoft glitch and knows of a secret hotfix or special trick to prevent it. I attempted to call Microsoft and it would be more enjoyable to punch a concrete wall since you're dealing with useless people
in a foreign country who can't really comprehend the seriousness or technicality of the issue, and don't really care, and aren't skilled enough to provide
insight.
Does anyone know about this problem?

Answer 1

Thank you for the reply.
I understand the flash you are receiving while launching Excel or Word is very fast. However just wanted to check if it is possible to get a screenshot of it.
Also, are you able to work fine on Excel or Word even after receiving the flash.
It seems the Office installation might have not been done properly.
There is a possibility, everytime you Uninstall any application, there are still some patches left behind which could cause an issue while Installing the same application again or even after Installation is successful, it sometimes gives
issue while launching the application.
If you want to give a try, you may try to Uninstall the product using Offscrub by clicking on the below link & then can have a fresh installation again.
http://support.microsoft.com/kb/2739501
Please let me know the status update once done
Abhijeet, the box flash happens too fast for me to capture a screenshot of it but I believe it's similar to the smaller box activation process (enter your email).
Word and Excel work fine whenever this is observed.
I'm skeptical that this is a "not done properly" kind of scenario, especially when it applies to so many people and many have brand new computers. How can you take a Microsoft Office disc and install it improperly on a new PC? Or how can a person
go through Microsoft's https://officesetup.getmicrosoftkey.com/ setup, use the software for months and suddenly it stops working? If this is a 'not done properly' scenario, then this is a failing of Microsoft's
installation source. I can't reiterate this enough, the software works fine for people since installation date and then randomly stops working at a much later date (but many of them failed last month and this is a newer issue).
I'm starting to get frustrated again as I'd already stated we've used your linked removal tool in my first post and the problem has returned for another user by which I'd used it and reinstalled the product. The client who's PC we have now, one we'd sold
them, needs to be returned to them and while Microsoft Office is currently working, I was told that if this happens again, they're "going to throw the f#(*@ computer in the river". No joke.
If we're at the point where we've moved past evaluating logs, registry keys, or file versions or anything along the lines of a developer determining how this Microsoft bug occurs, then I'll return the system back to the client and hope for the best.
Three strikes and I'm out with this one but perhaps the delayed startup is the final solution... I just wish I knew for sure as we've had a bad year taking a beating for Microsoft's products and their support is the worst in the industry.
It's further frustrating that since I'd touched base with Microsoft via phone calls, the only person who's been able to provide any insight into the issue is me.