If the button is stuck, then first it needs to be unstuck for you to accomplish anything. As even if you could fix anything else, the button will be needed. Also that should not effect the charging.
First you need to see if the button is actually the problem. Try holding it down for 15 seconds or so, until you feel the tablet vibrate. See if it will actually turn on. If not, that doesn't mean it is damaged, it could just be without power.
Try a different power cord and see if that will charge the tablet, or try your cord on another device and see if it works. If it doesn't, you need a new one. If it does work on another device, then your switch may be damaged and need repair/replacing. And, it also could be a bad battery. Since that is an older device, it would not be surprising if the battery was also going bad.
If you feel comfortable doing it yourself, then you just need the part and the right tools. If you don't feel comfortable doing it yourself, then you would need to find a good, reasonable, tech in your area to replace the switch.