iPhone continously vibrating but not charging

I've had my iPhone 5S for a while and tonight I went into the wall to charge it and it started vibrating. It wouldn't stop vibrating so I figured I would turn it off and it should fix itself. This was not the case, and infact it isn't charging at all. It will vibrate 10-100 times in a row with the charging symbol going on and off repeatedly. After it stops, it shows that it is charging (has the charging symbol), but it isn't charging. The battery is slowly being drained. I could not find ANY questions on the internet related to this at all.

Summary:

1) iPhone won't charge

2) iPhone continuously vibrates

3) iPhone is functional (until battery dies)

Anyone have suggestions/knowledge of this? I have tried restarting different ways several times and using my MacBook.