Why won't my Insignia ns-5004bt speakers power back on

Hi @mrchristmassuit

You may have to open up the sub woofer and check if there's any damage on the power board e.g. hopefully it is only a blown fuse.

Looking at images of where the power cord plugs into the sub-woofer cabinet you may be able to just unscrew the inset there and remove the power connector and check if the fuse is on a board attached on the back of it.

If not you will have to open the cabinet to access the board(s) (power board & amp board perhaps)

If you can't see anything obvious, post some close up images of the power board (board where the power connects to) and post them in your question. Here's how to do this on ifixit Adding images to an existing question