iPhone 5 battery drain after keynote presentation using VGA converter

During the presentation, the battery was ok, only down like 5% and no heat at all.

But after the presentation and I unplug the vga converter, it became warm and the battery starts to drain very fast, 40% in 1 hour.

I tried to remove all active apps, still draining. I tried to restart it, pressing power button, still draining. I tried to hard reset it, pressing both power button and home button, still draining.

Now I am charging it and the charge is slow. I am guessing something is wrong.

Has anyone experienced the same thing? What should I do?

Thanks for the feedback.