Congratulations on your find, but why did you want a TRX125 in non running condition? Now you need to find another one in not so good of condition for the parts you might need.
Anyway, your only source for parts will be Ebay, Facebook and salvage yards. The only parts available from Honda are nuts, bolt, bearings and some gaskets. I can provide you guidance, advice, part numbers and can email you or upload service manual pages. You can download a service manual for $14.95 HERE
Just let me know how I can help you. BTW, the engine does need a battery to run - the battery only provides power to run the starter motor and some lights.
The first step in trying to find spark is to unplug disconnect the black wire with the white stripe going to the CDI box - grounding the b/w wire is how you kill the spark. The ignition has 4 wires; when the switch is on, it connects the red wire to the black wire to make the lights and starter work - when you turn the switch off, it connects the b/w wire to green (green is ground). When trying to find spark - my first step is to unplug the CDI connector with the b/w wire, turn the key switch on, put the handlebar switch in the run position and check for continuity between the b/w wire and ground at the CDI connector - if no continuity, the problem is usually (in this order); wiring connections (including grounding connections between ground wires and components and components to frame), spark plug, spark plug cap, stator, CDI unit, pulse generator, flywheel, flywheel key or something else including a combination of problems.