14-2 is good for 1440w, continuous duty, inductive loads, @ 120v, nominal. so your fine.
as far as taking apart a digital ballast, the only thing your going to be looking for is physical damage, unless you know how to use a multimeter and know how to troubleshoot at the component level.. a digital ballast (or any ballast) has no moving parts. however its possible to have defective parts, a bad connection pont, broken wires. ballasts are pretty simple devices; therefore they are assembled by pretty unskilled workers, usually. so its not uncommon to get one bad from the factory. it almost sounds like a bad connection/broken wire in your case however, due to the fact you say the ballast lights the mh conversion lamp, then lights the hps. that is indicative of a bad connection on the hps ignitor circuit, as if a connection has to heat up to make good electrical contact...