Looks like when you reassembled, you did not attach the tailpiece, so the plug pulled outwards. You may (probably did) mess up a spring or two.
Luckily, the lock can most likely be saved.
*Use a hacksaw blade, place the blade teeth downwards on the brass cap, so it bite when tapped towards the back of the core.
*Gently tap the front of the hacksaw blade with a small hammer tapping slightly downwards and towards the back.
*Continue tapping, driving that brass strip off the back of the core. (Be careful, as the springs may try to launch).
*As the strip moves backwards, the springs and pins will be revealed. Collect them as you go.
*Once the strip, springs and pins have been removed, the plug can be pulled out to the front.
The front chamber's key pin will still be in the pin chamber, so don't lose it!
To prepare the brass slider cap for reassembly, put it in a vise and tap it with a hammer so that it forms a slight "V" along the length of the cap.
Reassemble the core with the pins, springs AND TAILPIECE!!!. Place the cap on top of the core. Hold it down so that it compresses the springs and fits into the groove. Test both keys to be sure they work. If they do, tap the brass cover down with a small hammer, or very lightly squeeze it down with a pair of pliers. As it flattens, it should hold itself in place.
Everything should now be good to go! Good luck.
Gordon
Just when you finally think you have learned it all, that is when you learn that you don't know anything yet.