I had this same problem with my BLU Studio XL 2 phone. I solved it by removing my battery, waiting 10-30 seconds, and then putting it back and turning my phone on.
First, remove the back panel/ cover of the phone.
Since my phone had a built in battery, I needed a 000 Philips screwdriver, which I found at Radioshack as part of a kit. The same kit I used can be found on Amazon:
After removing the screws, I used one of the little blue plastic triangles to remove the mid-frame of my phone.
I removed the battery, waited about 30 seconds, then put it back in my phone, along with the midframe, the screws, and back panel.
I pressed the power button, and my phone turned on!!
It worked normally.
'''My suggestion to prevent this happening in the future is to not shut down the phone while charging.