One more thing: Are you able to disconnect the load (at the outputs of IC4 and IC5) before testing the circuit? A short-circuit on the output might stop the circuit from oscillating.
Come to that, you should check from the junction of D6 and C27 to ground, to make sure there is not a short. That would mean a short in either D6, C27 or IC4, IC5, which would stop the circuit from working.
Please be very careful when working on CRT scopes, especially around the tube and the EHT lead that connects to its body - the tube itself acts as a capacitor and can store a dangerous charge for weeks.
Regarding terminology, the part that you have removed is a transformer - exactly the same as a transformer that works directly on 50/60Hz AC from a wall outlet, but smaller becuse it is designed to operate at higher frequencies. The entire circuit belongs to a class of circuits called "DC to DC converters" - the circuit takes DC, turns it into AC (because, as you've found, the transformer won't do anything with DC) and then turns the AC out of the transformer back into DC.
Please don't be offended by Nigel... he can be a bit terse, but he's lovely really