Black burn marks on the end of the bulbs are not always a 100% indicator that they are shot. Many newer fluorescent ballasts, particularly T5HO have what's called an 'End of Life' or EOL feature. This will cut out both lamps on a two lamp fixture, even if one of them is still good. It's designed to minimize risk of fire or bursting the tube due to the ballast continuing to deliver current to a non functional tube.
If you haven't tried swapping tubes with known good ones, that will still be your best option for step one of troubleshooting and could save you some money & aggravation. Not sure it's a good idea to be looking for voltage at the output of a ballast at the endcaps. Very high voltage and without tube installed the circuit would not be complete anyway.
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