well, if you have replaced the battery, and any fuses, its time to break out the old multimeter.
since you replaced the battery, you already know how to open up the device
first start by checking voltages because, well, you can learn a lot and its a bit easier than checking currents.
make sure the controller board is actually getting voltage...this may take a bit of wire following but there will be a one or more red wires that go to the controller board.
does the display even "flicker" when you disconnect the battery, wait a minute, and reconnect it?
Is it completely dead, or just not responding to the power button?
if you plug in an input power source (ac or solar)does it respond (which means the "brains" are still there)...
you can disconnect all the power (iincluding battery) and actually check if the power button is working all by itself; this will take a bit of teardown probably.
if the display is working when you hit the power button can you enable the usb or any of the output buttons?
do you know anybody that has one locally and would let you put their controller panel into your case?
The tricky part in troubleshooting is trying to figure out if its a "fixable" problem, or not.
A simple bad switch, failed internal dc converter, even a bad transitor may be fixable; sadly if its the controller chips that tends to mean its dead and its time to check its wallet for anything you can take!! (in this case the battery is almost certainly ok and the wired connectors may be useful for future projects)..
Electricians are not the people that "Fix" broken electronics; appliance repair people replace major parts with factory or 3rd party parts...and hobbyist are the ones that are crazy enough to attempt board level repair!!