If your iPad has sustained damage as you describe, it is very unlikely to be usable in its current state. Unless the iPad will restart when connected to its Power Adapter, your iPad is dead.
For practical purposes, in lieu of repairing and returning your own iPad, Apple invariably exchange a non-functional iPad for a renewed/refurbished iPad of the same model and specification. The cost of the exchange is the same as would otherwise be charged for repair. Unless you have benefit of an active AppleCare plan, an out-of-warranty "repair" while expensive will be somewhat less than the cost of a replacement iPad.
As for out-of-warranty repair costs, Apple offers a fixed-price price repair. You can verify eligibility and cost for your region/country here:
iPad Repair & Service - Apple Support
If you have an active AppleCare+ plan, the cost of repair is reduced to a small excess/deductible fee.