If I am reading this whole thing right,..... you are loading your amp with one cab that is an 8 ohm load,... then adding another that is a 4 ohm load,....and your amp head is an output of 4 ohms,....... is this correct so far.???
if so,.... what you are doing by using both cabs at once, is adding the two together giving you an ohm load of 12 ohms,.... and since your amp has an output of 4 ohms, you are taking an awful chance of overheating your amp,....
the proper thing to do is to match the output of your amp,... that way when you want to use it for it's 300 watts, you will at least have that to work with,....
the problem is,... when you add more speakers,.... if you use other plugs on the back of your amp,.... you are adding ohms together for one output,.....
Try plugging the 4 ohm 15" as a piggy-back to the twin 10",.... by daisy-chaining the cabs, you are running them at a lower ohm load than doing it the other way,....
and as for the one 10" not working,..... double check the solder connection,.... and try taking a piece of zip cord, (common two lead wire),... and while a signal is being fed to the cab,... take the zip cord, and touch the contacts from the other speaker,.... if you get signal,.. it could be the connection, the soldering, or the wire,..... if no signal,.... it could be the voice coil,... but a speaker not working right from the factory sounds to me like a warrenty thing,... or at the very least,.. a replacement at no cost,....
I would keep trying to contact the place where you bought the cab.....
Steve