We've just had an interesting support call and, after some hours, found the solution to the problem so thought we'd share it here so that others might save time on the same issue.
Brand new PC - very good spec, not that it is relevant to the problem, but a joy to work on as it is a Fujitsu i7 PC with 16 Gbytes of memory and a Samsung 512 Gbyte SSD drive so everything is very quick in Windows 7 (the machine is licenced for Windows 10 also but LOB (Line Of Business) software at site means that this can't yet be used.
Everything was working fine on the machine and software installs of Adobe, Office, Dropbox and other utilities etc. and then Office stopped working. Outlook was in the process of downloading / synchronising email box from Office 365 Exchange mail when it all just stopped working.
The error we were getting was instant upon launch of Office, and we found that Internet Explorer (IE11) was doing the same. You'd click on the icon to launch and no - crash, not happy.
We went in circles for quite a while on this - was it DLL issues, was the problem due to DLLs? Would repairing / removing and reinstalling Office work or would 32 / 64 bit make a difference? Having not got very far, we escalated the issue with Microsoft. Their support for Office 365 is very good and quick and a testament to their dedication to customer satisfaction. About 30 minutes after logging the ticket, we had a joint remote session on the PC affected and I explained what we were seeing and what diagnostics we'd done so far etc. so that we need not repeat things.
Pretty quickly, Jibin (the Microsoft Engineer assigned to the ticket) asked about recently installed programs, so I replied that it was all very standard utilities and software we often install on machines and all good and clean (known sources and corporate licences). We had a look at Program Files and Jibin asked about one that evidently popped out at him on the list, which was: Displaylink - which I did not particularly recognise or recall having installed to the best of my knowledge. Jibin went on to explain that this software is often automatically installed by external screen hardware like USB docking bays and external screen drivers. The version that we had installed (probably from something like a USB Dock being plugged into the computer) was version X and that he'd seen this before. We uninstalled the software (a few clicks), downloaded the latest version from http://www.displaylink.com/ and installed.
After a quick reboot, everything worked perfectly and normally again. I'm very glad we logged this ticket as searching on the net for the problem was in this case bringing up blanks. So Jibin Samuel at Microsoft, thank you very much for your help and sharing your experience :-)
We'd not noticed the software as it is automatically installed by devices and sounds rather innocuous in name. Newer versions of the software are much better on this.
For anyone else, if you find that MS Office and Internet Explorer crash quickly, immediately after clicking on the icons and Office installs are failing, do have a look for DisplayLink in Programs and Features.
Good luck fixing this problem if you have the same problem.