Hey Juan,
I think you misunderstand what I mean on my previous reply, you just need to clear your browser cache and try do not touch any setting yet because I already configured for you.
Try watch my video here before you test :
http://screencast.com/t/wtNVu6Sgp
What I did is disable that `JavaScript` from the Auto minify section is because it seems like this Cloudflare compression Javascript on the page is not doing well and causing this issue.
Second I disabled those JCH optimise and cache system from backend, because I would like your Cloudflare server cached your composer page first. After that, I help you enabled those JCH and cache plugin, then reload the composer again, it should work fine now.
Can you give it a try and see is it work?
Note : Do not change any setting.