You can’t know the damage until you open it up.
Whether it turns on or not will tell you a lot. As for the physical damage, the bending on the lower chassis looks pretty bad. I’m not sure how you’d fix it up. Maybe 3D printing or hot glue and plastic? Whatever you try, I think its usability as a laptop will be pretty limited. Duct tape and a dream, brother.
@Luca
I say go for free airflow.
@Luca
Your best option is to get a new upper and lower case online and transfer all the parts. It probably won’t be cheap, and you might end up breaking something more if you’re not careful.
The board looks fine. If it boots up and the HDMI port works, you might just need a new housing or some duct tape. But if it doesn’t boot, does it show any signs of life?
If you don’t know what hardware you have, you probably don’t have the skills to replace the motherboard or screen. Even if you did, it might not be much cheaper than just buying a similar new or refurbished laptop. You could always take it to a local repair shop and get their opinion.
How did it even get to this point? That’s what I want to know.
Melt it all together and make a stand for your (new) laptop. The remnants of the old one can carry the new one like a throne, helping it cool better.
At least you get better airflow. 
Since it’s not turning on, something serious must be wrong. Does it show any signs of life at all? If not, you’ll probably need to disassemble it to figure out what’s going on. With impact and bending like that, there could be damage to the surface components. Maybe a cable got disconnected or the memory/SSD got dislodged.