If there is some cable routing part broken then it is unlikely you would be able to get the brakes to function simply by tightening - you would likely have to take up enough slack to bring the two ends of the housing segments into contact with one-another... approximately the length of the toptube worth of slack would need to be removed, and it is quite unlikely that you have that much extra housing to make this possible.
The most likely explanation is simply the cable slipping through the pinch bolt on the brakes. Also possible is the ferrule (cable-housing end) failed and the inner steel coil pulled through and your brakes are only supported by the plastic jacket. Less slikely but also possible is that most of the strands of cable have snapped and the cable is stretching before final failure.
Is this a new bike? If so, you should bring it back tot he shop where you bought it to find out what is going on.
One last possiblity - maybe the brake caliper had something that was not quite 'seated' and your hard pull on the lever snapped it into place.