if the two broken tape ends are visible outside the shell of the cassette, you can join them by using sellotape ( cut it down to size carefully). then copy that tape onto a fresh one or a cd-r, and don't use the broken one.
if you can't see the tape ends, you will have to carefully open the cassette shell by unscrewing the 5 screws with a jewellers screwdriver . you will have to thread the tape ends along the front side of the cassette, leaving them exposed, and screw it back together. Then you can set about jointing them
All this will be hard to do without breaking the cassette it if it is a sealed shell which some were -in this case, get a blank (screwed shell) cassette and open it up, discard the reels and transfer your reels into the new body. be sure to put in the thin transparent liner sheets both sides of the reels to avoid jamming.
romko, October 2006