Reset through a little hole in the case? It probably won't bring the tablet back on, but if it does, you won't lose any of your data.
If it doesn't come on, you can't back up the data - the device has to be running to back anything up. You can't do a factory reset (which will wipe your data) wither, because it has to be running to do that.
Try plugging the charger in for 24 hours, then try turning it on the normal way, with the charger still plugged in. If it comes on, back everything up (see below), then have a new battery installed. (And never let the battery get below 40%. Waiting until the device tells you to charge it is a good way of ruining the battery quickly.
For backing up:
App Backup & Restore for apps.
Helium for the data the apps save.
SMS Backup & Restore for your texts
Google contacts are backed up at
Google Contacts if you have contact syncing enabled, otherwise you can install
MyPhoneExplorer and back them (and your texts) to that.
Drag everything else to an SD card or a computer, the same way you'd drag any file. Pictures, music, videos, documents, etc.