TW -
Fluorescents are funny. I'm not sure what voltage you would expect to measure at the bulb contacts, but measuring it is not straightforward. My TM is in temp storage on the other side of town, or I would check for you.
I
think that when you first turn the switch on, you should get 12 VDC from
one of the four pins to ground - but not from the other three. This would be the preheat voltage, assuming these are preheat lamps (which I'm not sure of).
After a moment or so, you should get a high voltage (300 VDC?) from
one of the pins at one end to
one of the pins at the other end - but there is no way to tell which one, at either end. So you have several combinations to try. This would be the operating voltage. And if there is no lamp present, the ballast (which makes the high voltage) might not come on.
So you see why measuring the voltage is not as simple as it is with an incandescent fixture.
You might start by buying a replacement tube from WalMart - they are only a couple bucks.
Assuming the thing was made by ThinLite (which is my memory), you can buy replacement ballasts from
http://www.wind-sun.com/Misc_AE/Thin_Lite.htm.
In the end, though, it may be easier to simply follow dcrdark's recommendation, and buy a new fixture. Camping World, or Wind-Sun at the link above, can help you out.
Bill