I've dug through my 'wrecking-yard' drawer and found the answer to my mystery. It was a dropped 260 with a cr@cked back that i tested w/o a battery. When it was given to me, the battery was totally flat, but not dead [o/c], and the unit didn't power up without the battery connected [disconnected the battery to test it]. When i reconnected the battery and put it on charge it powered. I put it aside waiting for another unit to cannibalize. I've checked it again and it has a cr@ck in the board, making and breaking. If i push down hard on the board it powers on, but flex the unit a bit and it goes off. I guess reconnecting the battery was enough pressure.
I had my 300 apart back then too to fix the power button. I need to dismantle it again because the power button is still sticky, so i'll check it too w/o battery. But if the battery wiring is the same as other nuvis i'm sure it will also power on.
Sorry for the 'red herring'.
I suppose you might have a board problem of some sort too. Test the battery to ensure it's not shorted/open circuit, if it's ok then even it's been totally left flat for a while it will probably take a charge provided power is actually getting to it of course. 14xx are also very prone to damage to the usb socket and if it's come away from the board that could be your problem. Try gently wriggling the plug under connection to PC to see if it powers on, and while pressing the on/off button when you move the plug up and down. If that's your problem, they are very awkward to repair.
@Loly, I've used tiny strips of very sticky duct tape [the thin plastic, not the fabric type] to hold the three pieces of a broken 1390 bezel together on the underside. As long as the pieces have retaining lugs to hold in position that works fine too.
@dasil, I've found that plastic welding works fine but a really brittle bezel will just break again in a different spot if it has to be removed again.