I don't know.
I have always used a floating Dazer for this type of work.
Like this one.

They have been around for ever.
http://www.ebay.com/itm/mh-20-Vintage-Dazor-2-Tube-Fluorescent-Swing-Arm-Clamp-Mount-Desk-Table-Light-/121298872734?pt=LH_DefaultDomain_0&hash=item1c3df9e99eI looked at the bulbs and as far as I can tell they look like the typical 15 watt T8 bulbs.
Do all the ends light up when you hold in the start button?
Is the indentations on the bulb end caps lined up with the center of the bulb holder?
Sometimes on new bulbs the button has to be held down for a while to heat up the filaments in the ends of the bulb so when you release the button the arc is struck inside the bulb.
I have a 1970s type two 15 watt desk fixture with new GE bulbs that I have to hold down the button for a while before releasing the button to get them to go.
Other wise it won't start.
If you get it to start, I would let them run in for a while.
If it was working before the bulb quit working it is my guess that the fixture is ok.
I would check all this above first before digging in to it.