Have you used the cleanup utility to remove the previous installation completely - if you have not tried that I would do that first.
I had a similar issue a few weeks back with another user - I could not resolve it, however the customer persevered and looked up problems using Google and found a restart method that allowed them to suspend things that were running at start up so he could get the install to work - if your computers have had recent rebuilds you need to check the following
1) Do you have all the Windows Updates installed
2) Do you have the latest Graphics Driver installed for your Graphics Card
3) Do you have all the latest System Tools, Bios, Drivers etc installed from your PC supplier eg Dell
4) Have you run Cleanup to clean out any old installs of TBC 100% so you have a clean start point
If you are running WIndows 10 - you can tell the installer to not install DirectX as that is installed and managed by the Operating System in Windows 10 and that is sometimes the thing that stops the installer from working
If when you have done all the above you are still getting a blockage of some kind, you may need to restart your PC in Safe Mode or this BIOS change at Startup to suspend things that are typically run on Boot Up to enable TBC to install - that is fairly rare that we see this and is normally caused by some system incompatibility with your computer setup - I apologize that I struggle with those things also when they happen and often Google (while it may take time to find the right answer) can often provide some insight as to what you may have to do to fix it.
If you need further help, then I would raise a Technical Support Ticket with your dealer and get the Trimble Support team involved as they have more experience in troubleshooting Installation problems once they get above the usual steps that I go through with people - in most cases those steps above will get people working - the Bios issue etc is a last resort.
Alan