These instructions show you how to open up your MagSafe connector and fix the internal connections.
Step 1: Unplug Everything
Unplug you charger from the computer and the wall.
Step 2: Cut Off Outer Housing
The outer housing is the white shell on your connector as shown on the the right in the image. Use a very sharp knife and very carefully repeatedly score the sides of the outer housing until you cut through it on all sides.
Step 3: Pry Off Outer Housing
There may be some glue behind the outer housing so some prying is necessary to remove it.
Step 4: Cut Off and Remove Inner Cover
The inner cover is made from softer white plastic (shown in the middle of the image). Cut on all sides to remove.
Step 5: Inspect Wires
inspect wires to determine which ones are broken
Step 6: Cut Back Wire Insulation
remove metal collar and cut back about an inch of wire insulation
Step 7: Prepare Wires
the wire that runs down the center of the cable connects at one location. The bare wires around it connected two locations. if the bare wires are broken twist them into two pigtails that are long enough for reconnection.
Step 8: Solder Wires
Tin the end of the wires and the locations that they will reconnect to.
then solder the connections making sure that the wires are routed so they group nicely at the cable.
Step 9: Test the Connection
Step 10: Retest Connection
put the inner cover on and then the outer housing
Step 11: Apply Tape
use plenty electrical tape to keep housing together and strengthen connector to transition. build up tape thickness around end of housing and create a taper so that any bending of the cable happens away from soldered connection.