The power button is attached to the keyboard. There is a good chance it is only the keyboard that is damaged. If the keyboard is damaged it won't enter the keys you are pressing so you can't enter a password.
Here is what you can do to confirm if it is only the keyboard or if the logic board is also fried.
First, get a USB keyboard, any one will do it doesn't have to be Apple. Then go to ifixit.com and find a guide on replacing the keyboard on that model. Follow the guide to open the bottom of the MacBook (literally removing 8 screws). Then look at how to disconnect the battery to shut it off. Then look how to disconnect the keyboard. BE CAREFUL. You will need to disconnect the ribbon cable that attaches to the logic board. Now, put the bottom back on making sure the ribbon cable doesn't get pinched (it shouldn't but I put a little tape on it just so it doesn't snag). You can plug the battery back in too but it isn't necessary just know that it will keep you from closing the cover fully and that is okay. Now, plug in the USB keyboard and connect the AC adapter. If it doesn't power on then you need to search on Google on how to start that model without a power button (some say you can unplug the battery and when you connect the AC adapter it will power on, or you need to find the 2 solder points that you need to bridge to get it to start). Anyway, if it boots normally with the USB keyboard attached then you are golden and a new keyboard will fix you up. If not, then it can mean further damage is done and you may need to completely remove all parts and clean and dry them. I have had some success doing this and removing rust from the logic board and had a fully functional system after.
If you don't feel comfortable after looking at what it takes to replace the keyboard then you probably just want to find someone like me to pay to replace it for you.