Vacuum hose fell off, will not turn on with battery charge?

Hey, I'm having a few issues with my vehicle listed above and if I'm being honest, I really don't know much about engines.

1. I found what I think is a vacuum line burned through and not attached to anything on either end. No idea where it goes.

2. Even though the battery has a charge when I put the key in it won't even turn on.

Before it completely stopped working there was some electrical flickering and glitching. From what I checked out on YouTube, it looked like an ignition switch problem? But after finding the vacuum tube idk. I have pics as well.
I appreciate your thoughts.