Not sure if this is exactly the answer to your problem but give it a go:
You have 10 switches. Put 5 on and 5 off. Does it work? If yes then the fault lies with the 5 that are off.
Reverse the switches (On to Off and Off to On). It shouldn't work. Select 3 of the ones that are now on and put them off. Does it work? Then one of the the 3 switches are duff and so on ....