Unlike the iPad mini or even the iPad 2, the iPad Air rarely loses its backlight. I repair mail-in backlight problems every day and I've only ever seen 2 Air backlights that were board related.
A backlight filter change is not an expensive repair to send out for, it is more of a tool. If you try to do microsoldering without the right tools it is easy to ruin the board.
First, like Eric suggests, you should try a hard reset--or just lift the board up off the battery to reset it. That will solve most problems that are not related to the LCD itself. There are quality vendors that have fantastic return policies if you want to just try a new LCD. Stay away from eBay and Amazon for parts and you'll do fine.