Home and Power buttons not working

The first thing I will say that a lot of people don't realize, is that rice will ultimately make your issue even worse. Rice absorbs moisture and will trap any existing moisture inside for much longer, so you should not be using this iPad, even if it's been days since putting it in rice. It sounds like the buttons have been shorted. What you need to do is remove the glass and LCD and use isopropyl alcohol to clean off any corrosion and dry any water left inside. Let it sit 24 hours before testing it, it could be damaged connectors, buttons, or parts on the board, there is no real way to tell without looking inside.