Hii

The official link for login page is http://mbbs.aiimsexams.org/
Visit this page and try to login but before that make sure that you clear the browser cache. Secondly try to login in non peak hours like late evening. That time there would be less rush on the site and it would work properly.
Also make sure you are using a compatible browser i.e Chrome, Firefox 3.5 or internet explore 9 or above. 
Even if the problem persists, then contact the aiims authority and convey your issue to them. You can contact them using email - aiims.mbbsexam2019@gmail.com

Hope this helps
Thanks!