Sadly this issue keeps coming up with some Samsung tablets, and occasionally their phones as well.
Hmm. I would try seeing if it will connect to any public wifi. Say at a library or cafe. If it won't there could be a couple of reasons.
The time and date on the devices could be not reading correctly. Strange as it sounds, this can cause it. So you need to check this on both the tablet and the modem/router. Also, make sure the modem/router is also set to be in the states and in your correct time zone. You would be surprised how many times it isn't. And while your other devices work fine, this could still cause issues with the tablet.
Another option is to restart the modem/router and restart the tablet as well. Yes I know it works with other devices, but it can't hurt.
I would also suggest making sure that the tablet is fully updated. Check for any firmware updates. You can connect to a computer, via USB, to do this if the wifi is still not connecting.
One more thing to try, the antenna in the device may have come partially or completely loose. Can happen if knocked around, dropped, or it wasn't ever really secured correctly. To check that you would have to open the device and make sure it's connection isn't loose.
This link to the manual for the device should help you as well.
http/cache.vzw.com/multimedia/mim/sam_galaxy_tablet/sam_galaxy.pdf