Greetings Jak:
I just brought up your site administration (with the info provided) and was able to bring up the Menu Manager->Main Menu->Menu Items->Add New Item->Menu Item Type (clicking “Select”) without any issues. When I clicked the “Select” button next to Menu Item Type, the pop-up box with the list of selections came up as it should.
Just to be sure, I tested this within FireFox, Chrome and IE browsers.
So … unless I am misunderstanding your core issue … you’re saying that – using a regular desktop/laptop computer – you aren’t able to complete the above steps?