New lamp but still no picture

Recently my television stopped coming on. After reading the insert sheet about the lamp indicator, I realized the lamp indicator was on and that I needed to replace it. After removing it, it was obviously bad, there was now a big hole at the front of the lamp and little ***** pieces of glass were stacked inside.
I ordered two replacement lamps from an after market vendor. After putting the first lamp in, putting back the lamp cover back on, plugged the TV back in and powered on the TV. However, no picture was displayed. Both the Power light and the Lamp indicator were flashing. Unplugged tv, removed the lamp cover, took out the lamp and reset it in the plug and replaced the cover. Plugged it back in and powered on the tv. No pic. This time, did the same steps as before, but used the second lamp. The picture came up immediately as expected. I then returned the first lamp to the vendor stating that it was defective and asked for a refund. They ran their own test: "Lamp held light for the duration of the test. Lamp will be tested again after proper cool down period." After the third pass, the lamp was declared not defective. The manager stated that they used a lamp ballast from the manufacture that test the lamp for defects. Therefore, they charged a 25% restocking fee. My question is, what determines if the lamp is defective?