Wow thankyou!
I love how much of it is power supply. Literally a tiny DSL router in bridge mode mated with an oversized laptop brick. Keeping some of the input protection in a tin can is cute (blast containment?)
If it died due to a storm: I would start with a DMM to inspect the DSL input protection parts. If they have done their job correctly ("if") then they may have sacrificed themselves to save the more sensitive ICs. Gas tube should be open, fuses should be short, capacitors should not be shorted and transformer/choke windings should be distinct (the last two may require desoldering to test).
If that doesn't yield anything obvious: check to see if the relay has welded/exploded inside. You can try and probe it whilst the unit is running, or try and cut the plastic cover off it for a visual inspection (often they don't fall apart and you can watch them working, but it depends on the design). A little bit of darkness on the contacts can sometimes be normal, but anything more than that is suspicious. If the relay has welded or exploded then the modem ICs have probably been fried too and you are probably SOL for the repair.
I see four unpopulated pin holes on the DSL board. There is a good chance that is a UART port. Basically all DSL modems have a 3.3V UART at 9600 or 115200 baud 8n1 that gets spammed with boot and operation messages, sometimes these can give you a hint as to what is going wrong (eg "no carrier detected" even when plugged into DSL line). If you're super lucky they also provide an interface you can get a full shell on for full router control. Buy a cheap USB uart if you don't already have one, three jumper wires (GND, RX, TX) is all that's needed for anything reasonably modern (the 4th pin will be 3.3V or 5V, which you can safely ignore). Use a DMM to work out which pin is which. Try different combos of RX and TX until something works. Try different baud rates until you see something other than gobbeldybook appear in your terminal program.