Just so you know, a trial version is simply a full version waiting to be activated. All you should need to have done was to activate the trial version you already had installed using the serial number from your purchase.
While I do not know if it applies to your situation, you might try running the CS Cleaner Tool AFTER you uninstall whatever you have installed now and see if that helps clean things up for you to install successfully.
Adobe Creative Suite Cleaner Tool
helps resolve installation problems for CS3 thru CS6 and for Creative Cloud
The reason I didn't just activate the Trial version as a Full version was because the only option for doing this that the Adobe website gave me was to download the Creative Cloud version and pay a monthly fee. I do not want to pay a monthly fee as I do not want or need all the other stuff that comes with that. Hence why I went out and purchased the Full version commercially.
I will try the CS Cleaner tool that you have provided, but please forgive me if I sound sceptical about the potential success of this. I have had such apallingley poor service from Adobe today that I am reluctant to trust anything the company says. However, I will try it and if it works as you say I will let you know via the Forum.
Well I followed the instructions you supplied and after downloading the CS Cleaner Tool, ran it, restarted my laptop and then reinstalled Lightroom 6.
Unfortunately, there has been no improvement and I am still unable to use Lightroom 6.
Unless this issue is resolved in the very near future I will be returning the software to PC World as unfit for purpose, and demanding a full refund.
Moving this discussion to the Photoshop Lightroom forum.