The first thing I did was do a quick google and I can see that you've also posted on the Prestashop forums. Good work on that (that was going to be one of my first suggestions as they will know Prestashop better than me).

A quick google shows that the theme you are trying to install "Alysum" is a paid theme that comes with 6 months of support. So I suggest that you contact the developer and use your free support. The fact that it isn't showing any errors suggests to me that the issue is either config (perhaps additional steps need to be taken as suggested on Prestashop forums?) or the theme itself has a bug. Although that's really hard to confirm without having access to the theme.

If you can reproduce your issue with a free theme, then please post info regarding the theme and I'm happy to have a closer look.

As per the Prestashop forum, it's worth double checking the theme install instructions (if you haven't already).