It could be the secondary load is too large for it to oscillate correctly. You'l notice a FB loop from the Focus pot that controlls secondary voltage, All high value resistors should be checked as they drift in values. HV caps are suspect too, sometimes they just fall apart when touched.
DC restorer diodes sometimes fail but these normally have a high Vf and can be tricky to test.
IIRC a recent thread on a TEK 465 had a shorted PDA multiplier, disconnect yours and see if the HV fires up.
Hope these are a few clues that help you move forward.