Can we fix it? You bet! cost your time. In reality it is a cheap low powered motor that sells for about £1 and not worth the effort if you have more money than time but having gone to the trouble of salvaging it you may as well fix it and you never know when you might have to fix it because you need it, and the principles apply to other motors as well
Step 1: clean it
If it needs it clean it with scotchbrite and soap to remove any corrosion and goo it doesn't matter that it gets wet you're going to strip it completely and dry it thoroughly anyway. DO NOT leave the scotchbrite in the kitchen sink to be used later to clean pots and pans copper salts are toxic and the contacts/brushes may well be beryllium copper as it has spring qualities and others that are useful in this application BUT beryllium compounds are also toxic and cumulative poisons, so wash your hands after as well
Step 2: take it apart
Place a small blunt blade between the drive gear and casing and leaver the gear off. Using a very small flat bladed screwdriver unbend the tabs securing the back to the case and pull it off. Push the drive shaft down on the table grip the armature and with draw it from the body of the motor it will kick sideways as it comes free.
Step 3: clean and examine
I used disposable paper tissues for most of my cleaning kitchen towel or cotton rag would work as well.
Notice the green goo the colouration is due to copper salts and possibly beryllium salts both of which are toxic ( I am possibly over stating this but it is better that you know than don't)
Check the brushes are intact if not there replacing them is not impossible but is not covered by this instrucable set aside for further work.
wipe clean the commutator armature and shaft assembly use a solvent if required, I tend to use lighter fuel the liquid type not gas as my cleaning solvent of choice isoprop will probably do as well but avoid acetone/cellulose thiners or white spirit as these could damage cheap laquer on the windings. The bearing surfaces shoud be smooth and bright.The armature (large & in this case 3 lobed ridge section) should be free fron rust. The Comutator (short brass section on the left before the large black ring) this should be free of obviouse ridges smooth and have a clear gap between each segment. The small brass ring to the right of the armature is a thrust race this stops the armature comming into contact with the motor casing. There should be no visible broken wire or signs of burning on the windings and idealy the continuity of the windings should be tested with a multi meter or a lamp/LED and battery ( a step I forgot until doing the write up I just glanced at it and decided all was fine)
Turn your attention to the case clean inside check there are no metal /rust fragments sticking to the field magnets and that the magnets are secure.Twist up a small taper and clean the bore of the front bearing in this case it appears to be a nice little oilite type bearing this could be a useable scavenge if the motor is unrepairable.
On larger motors say a car starter motor reconditioning is possible with patience files emery cloth wire brushes and scotch brite on a motor this size your opptions are much more limited metal polish rag and a scraper made from a sewing needle are about your limits.
I have come across articles covering rewinding the armature of a motor from a CD drive to make a higher powered motor for a model plane so all things are possible but other than as an exercise in can I do this is it worth while?
Step 4: repairs
All motors will be different but on this one the brush carrier is a separate unit from the back plate located on a pin and in a slot in the back plate to remove it was simply a case of putting my thumb nail in the joint and pushing you may wish to use a small screwdriver or knife blade.
clean the back plate and brush carrier again I used lighter fluid and tisue paper.
Source your replacement cable I used a strand from an old ribbon cable, strip a short length of insulation and bend the stripped end at a right angle. Gentley prise the brush from the carrier and push the stripped wire down into the locater slot push the brush back on top of it, bend the wire round the bottom of the brush carrier and trim it off. I find small nail clippers make good wire cutters and can be used for stripping insulation as well onec they have been used in this manner they are useless as nail clippers. Whilst you have it appart rewire the other brush to.
Step 5: reassembling
apply a drop of light oil to the front bearing shaft grip the armature and commutator assembly by the commutator and reinsert into the case keep a firm grip on both as the field magnets will make it kick around. Apply a light smear of petroleum jelly(vasaline) to the commutator if the motor has carbon brushes do not grease the commutator.
Next Do Not use any more force than you would on a touch screen, place the rear bearing shaft at the top of the V formed by the brushes and push in until it touches the back of the case at this point the commutator should have just entered the brushes. align the shaft with the rear bearing bore and push together. Once the shaft can be seen in the bore and the back plate has engaged with the case slightly more force may be required. check the motor spins the apply power to test once you have confirmed the motor is working recrimp the tags holding the back plate on. They do not need to be over tight if the motor won't run after you have recrimped the tags gently losen them as you did when disassembling. I refitted the drive gear as well just so I didn't lose it it would probably be a good idea to secure the new cables with hot melt glue or epoxy resin as they are only a friction fit and will not stand being pulled very hard or at all.
Step 6: other motors 1
having recently rationalised my pile of salvage cd drives into useful parts I thought I'd open one of the small motors up to show the intervals of small brushed motors are similar. This one (there are actually photos of 2 different motors here one with attached wires one that was soldered to a pcb) operated the tray mechanism. The back plate was staked in (the case is pressed in enough to stop it coming off and moving) this took careful work with a pair of small side cutters to undo. I then inserted a small screwdriver into what is the cable port on the wired version and twisted to remove the back plate. This not only bent the back plate but also damaged the field magnets (which appear to be the flexible strip used on magnetic display boards) as I inserted the screwdriver beyond the case. The brushes in this case are just fine wires this meant the armature assembly has to be inserted into the back plate before the case on reassembling. their position checked and adjusted using a sewing needle. Once reassembled the back plate was pressed back in place using long nosed pliers and a safety pin as a spacer a small nut or a stack of washers would have done instead. This also straightend the back plate and the motor remains functional despite the damages caused in dismantling.
Step 7: larger motor
this step will be added next time I have cause to disassemble something bigger.