I looked in the "Tune Sheets" book and the supplements by Bulleid and
that particular tune card is not there.  It's typical of the
multi-colored tune cards of the later date boxes, but unfortunately not
attributable.

As for the starting problem, it's a typical problem that occurs when
one or a combination of things happen over time to a governor (the unit
that comprises fan assembly and gears).  The most common mechanical
causes are:

1. a divot in the jewel,
2. a flat spot on the pivot of the worm where it meets the jewel,
3. wear on the worm and/or the worm gear, and
4. worn bushings.

There is _only one_ adjustment screw in your governor and I implore you
not to touch it!  It controls the mating of the worm and worm gear
and moving it will not solve your problem, but could create a lot more
of them.  You could easily cause a 'run' in your box if you move the
worm too far away from the worm gear: the cylinder would then spin (or
'run') in a millisecond with whatever power was in the spring.  This
can cause massive pin damage, tooth and tip breakage and gear
stripping.

In order to 'restore' a piece of machinery you have to disassemble it
and remove all the old grease, hairs, bug carcasses, etc., not just
oil it.  By oiling without cleaning it, all you're doing is creating
a sludge that will work for a while, but will actually cause more wear
because it becomes an abrasive.

There are many ways to clean the cylinder.  Again, it has to be removed
from the mechanism in order to do it.

If you're determined to do the box yourself, might I suggest that you
call a qualified person or purchase a repair book to give you some
guidelines.

Let me know if I can help further.

Nancy Fratti - Nancy Fratti Music Boxes
Canastota, New York, USA
http://www.nancyfrattimusicboxes.com/