I think an autopsy is in order Dr Mallard! [are you an NCIS fan?]. Good advice again from dasilvarsa. Most likely it's hardware failure, i suspect there is some common component in 37xx hw which fails because every now and then one will defy all efforts of recovery and remain 'dead'. You could try flexing the board a little while powering on but even if the pcb is cr@cked or if it's a 'dry-joint' type of fault it's toast anyway imo. Boards aren't worth messing around with these days ....

You and i must be living in parallel universes. I had a 3790 in bits in my parts drawer which i bought cheap a year or so back as 'For parts or not working' on eBay. I couldn't coax it back to life. Individually the screen and battery work with another 3790, but known-working battery and screen won't work with its board. Gone coon. Picked up another 3790 on eBay just recently described as the screen having 'bubbles at one end', this one:
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The traffic receiver and mount alone are each worth what i paid for it. Quick screen switch from the dead one and its all good.