Hi Hugh
Well thats some good fault finding you have been through there! It is quite common for the 3.5mm socket on the pcb to become loose and loose its connection (often it is fine while the cymbal wire is in one position but it the cymbal wire moves a little bit it looses the connection) This is caused either by the vibration of enthusiastic drummers or by having moveed the cymbals while the wires are still connected. You can resolder the 3.5mm socket back onto the PCB if you believe this to be the case but it will not take much heat before the solder points on the board come away so only use a very low powered soldering iron (15W) and be quick about it!
Another thing you can do is to put a new 3.5 mm socket on the other side of the PCB (you can see they use the same PCB for left and right side cymbal) but this often involves drilling holes in the other side to put the solder pins through the board and then you will need to scratch the coating off the PCB around the holes you drill to reveal the copper surface under the green coating which you need to solder onto. This is a difficult job involving a tiny drill bit and some very delicate scratching (DJ Hero pun anyone?) but can be done. Otherwise you could look at hardwiring the cymbal by soldering the cable directly onto the sensor wires but this is even more difficult and you will not be able to take the cymabl off to move the drum kit anywhere.
The only other option is a new cymbal which you can get
hereHope this helps - tell us how you get on