If you connect the iPad Mini to your laptop, is it detected by iTunes?
If yes, see #4 below.
If not, the following may be damaged:
1/ Lightning connector;
3/ Components soldered to the board ("burnt" components) e.g. logic board;
4/ LCD (less likely) and touch screen;
5/ All of the above.
The LCD, touch-screen, and batteries are the parts that you can replace without having micro soldering skills and/or enough knowledge of such devices to troubleshoot the board and lightning connector.
Once done, you may still have a brick on your hands.
If you feel up to it, here's the guide to try the replacements. Or, if available, you may switch logic boards with a known good iPad and tell us what you see working or not working.
My advice? For this very unfriendly device with this type of unfriendly breakdown (liquid damage), let someone trustworthy (such as jessabethany, member on on this site, search for her) and with the right skills, tools, and knowledge examine it and give you an estimate.