It does sound like you'll need to re-flash the ROM for your tablet to get things working normally again. If you go here:
https://updato.com/firmware-archive-select-model?exact=1&q=SM-T280
and find your country and your carrier, you'll need to download the ROM that matches your tablet (file size will probably 1GB or more). The download page for the ROM you select has basic instructions on what you need and what to do. You will need a access to a Windows PC too.
https://updato.com/how-to/how-to-install-an-official-samsung-stock-firmware-using-odin
Basically you need to install the proper Windows driver so it detects your tablet properly, you need to download and install the Odin utility (it's only 2-3MB in size), use a USB cable to connect your tablet to your PC, and then use the Odin utility to flash the ROM you downloaded onto your tablet.
-- The instructions refer to a newer version of Odin, you might have better results using an earlier version, 3.10.7 works well with Lollipop for instance. Odin isn't necessarily the best when it comes to backwards compatibility so using the latest version on older hardware often results in odd error messages. Here's a good source for whichever Odin version you need:
http://www.droidviews.com/download-odin-tool-for-samsung-galaxy-devices-all-versions/
-- If you need a valid driver, try installing Samsung's Smart Switch. It will automatically install the proper driver along with the Smart Switch utility itself.
https://www.samsung.com/us/support/owners/app/smart-switch
Don't start up the utility though, you'll get better results using either Odin or Smart Switch but having both running at the same time might result in a error as both utilities are using the same system resources and conflict with each other.
-- If you don't have access to a Win PC, there's also Heimdall, an alternative to Odin and available for Linux, Mac, and Windows. Functionally it does the same as the Odin utility but some of the menus are different to you just need to adjust things accordingly.
https://glassechidna.com.au/heimdall/