I'm not with Laminar Research, just a fellow simmer in the UK, but a couple of questions:-
1. Does your internet connection work normally with other applications i.e. the internet & other downloads etc?
2. Do you have any anti virus/malware software on your PC likely to be blocking access to the LR website?
3. Do you have a copy of X-Plane 11 on your PC already and if so, where did you purchase it and in what format i.e. digital download, DVD, Steam etc?
4. Could you upload a 'screen print' of your monitor to this post, showing what happens when you try to download the demo version of X-plane 11?