So I guess they wanted to replace the screen. But...I'm not sure it is the screen. I mean, if there was no drop, if there was no water damage...if it doesn't even charge, I'm pretty sure it's not the screen. It could be the battery....or something on the motherboard. Maybe the charging port itself, but unless you played with one of those USB killer devices, I don't think that's it either. So, the port is not fried, the battery could be dead. But to be honest, I've never seen this particular behaviour before. Aaand the last possible cause of the issue could be one of the components on the motherboard going bad.
Do you remember if the phone was charged when it went blank? Also, how old is your battery? Is it the original battery that came with your phone?
Anyway, if that price was for the panel (I'm guessing they want to replace the screen), I would say that's probably not gonna fix anything, since it can't be the screen if the phone doesn't turn on at all.
So, I'd say could be the battery (but not really likely), could be the port (but also, if you didn't use any special charger, or a third party charger not meant for this phone, or stuff like that, it's also unlikely) aaand...last but not least, the motherboard.
Unfortunately, Apple doesn't do motherboard repairs. They will either swap your phone entirely, or replace components, such as the screen. But they won't touch the board. If your phone is still under warranty, I would suggest to go to an Apple Store, or an AASP, and see if they can replace the phone. If it's not, sadly there is no way to fix this with Apple. There are other places who offer this kind of services, but this will also revoke your warranty (if it's still under warranty) and out-of-warranty benefits. Because it's considered "unauthorised intervention on the phone". So...choose wisely. :)
If you got nothing to lose anyway, I guess it doesn't really matter which one you choose. But I'm just putting it out there so you're aware of this. :)