Its hard to determine what makes a ballast go bad. It could of been poorly constructed, could of been damaged by a multiple of things. Water, impact, surge, heat. Does it normally buzz when it use to light? I for one am not impressed with the insides of my Current 1x55watt fixture. I've never had issues with it though, I built a fixture using a AHsupply kit. The wooden housing I made may not be as pretty as the Current housing. I trust the one I made more. It has much better ventilation for the ballast. It also got pulled off a 55gal tank once by a kid. The impact knocked the 2-55wat compacts out of there holders, but they stayed lit the whole time.
If you get the voltage meter, set it to the highest possible AC voltage. Test at the bulb socket. The output voltage should be printed on the ballest. It should also be high, most likely higher than the voltage meter will go. If the meter is older(not digital) be careful. If it reads the highest it can go, disconnect it. If it is an older one and you let it max out for to long it can damage it.
A bad light may make the other one not work. I am not sure on this though. I took one of the bulbs out of the fixture I built and the other one lit no problem. Ballasts differ though.
edit: when testing the socket without the bulb in it, you should get a very high reading. I tested my 1x55 ballast and it went off the scale when the meter was set at 1000v AC. Put the bulb in and also test it, (even if it won't light). To do this put the bulb in the socket but leave a gap so you can see the pins on the base of the bulb. Test at the pins. When the bulb was lit my meter picked up a steady 400v AC. Try not to bridge two pins when you do this, it will stop the bulb from lighting.