My iphone vibrated when i plugged it in but the screen won't turn on?

My iphone vibrated when i plugged it in but the screen won't turn on?

Added (1). i turned on the screen and it was frozen then i clicked the power button and the screen turned off but wouldnt turn back on, then i pluged it in and it vibrated like i had set it to do but it won't make the charging sign on the screen. Also its an iphone 4 so kinda old but it was working perfectly before.

What type of phone is it?