You have unfortunately jumped from one undocumented product to another, the Chinese TB boards are noptorious for their lack of documentation or if they do have some it is often incorrect.
Regarding Mach and the licence. First thing is the licence is very likely a pirate licence. Second is even if it is a legitimate licence they are non transferable so really you should be trying to set things up in Demo mode, ie delete the licence from the Mach folder.
Regarding your computer death, highly unlikely that could have been caused by connecting the TB board unless there are serious issues with it and it is sending high voltages into the port, even then I would expect the port to blow but the computer still be ok.
As you have no problems with the third computer then I would say its just all been coincidence.
What would I recommend, well probably nothing you want to hear

Get rid of the TB board and buy something like a Gecko G540 or some other well known and proven board, many have had to do that and have not regretted doing so. What they have regretted is buying the TB in the first place and wasting money.
Of course this is just my opinion and observation but when I first started out I did similar, TB boards were not around then but I purchased cheap drives and breakouts from USA eBay, I had nothing but issues and problems and despair until I got a loan of a Gecko drive to test and the machine was transformed, it went from a very unstable 400mm/min to a very stable 4000mm/min, I immediately ordered some G201's and junked the rubbish I had been using, lesson learned for me, sadly I see it repeated time after time with new users

Hood