Wm 10 type walkmans are slightly difficult to mend because of their tiny size.
You can download the service manual attached at the end of this post to give you a clear idea of technical details
Here are some pointers/tips
1)OPENING UP: a)unscrew the 2 central hinge screws to remove the cassette door
b)unscrew the 4 chasis screws on the four corners of the back
c)unscrew the ornamental dial of the volume control (using tweezers in the 2 holes or a pair of pointed scissors)
d)remove the battery cover and battery
2)'NON WORKING'???: If the unit doesn't power up there are 3 common things to look into before ripping things open & worsening things:
a) plug in a pair of earphones to complete the 'power on' circuit/power saving feature
b)If an old belt is jammed it prevents switching on/powering on...replace the belt
c)simple corrosion: Corrosion is mainly seen towards the -ve terminal..scrape off with a sharp blade/emery paper or use commercial dissolving solutions
d)BAAAAAD corrosion:-)): The whole battery compartment and surrounding areas look swamped with the ooze...clean up and carefully unscrew the circuit board to check underneath....the wire from the -ve battery terminal to the pcb gets disconnected by the corrosion eating into the point of soldering.
3)SCRAPING/Scratching/Freewheeling NOISES: Sony provides felt spacer strips stuck onto the inner surface of the metal shell of the walkman and also on the surface of the pcb to maintain a certain distance to prevent scraping of moving parts with the shell. These spacers get powdery with age & can be replaced quite easily
4)Headphone sound problems. The supply to the headphone socket is via a flexible pcb which sometimes goes kaput in one of its lines.Either link a thin wire from start point to end point or if the break in connectivity is located bypass it by carefully scraping the protective varnish on either side and soldering a small wire segment