I've got a 3790 with identical symptoms [won't charge by any method, powers up with another battery]. I bought it cheap for spares mainly to get the screen. Original battery is ok and working now in another unit so i guess it's got the same problem as your 3490 Loly. I suppose the fact that they won't charge by either the powered mount or microUSB port is a sure indication of a board malfunction. But it looks like big-time micro-surgery to replace any component on those boards.