This happened to me too.
My iPod touch 2nd Gen had a broken digitizer but still had an intact screen. The backlight was unaffected and was still very bright. But after replacing the broken digitizer, the backlight didn't come on. I tried shaking the unit, hitting it on my palm, until eventually I gave up. I left the unit ontop my desk, it went into standby with a clear screen, then I woke it up from stanby and the backlight just magically turned on.
The iPod touch from versions 1g to 3g, as of what I have read, have ccfl lamps (a.k.a. a tiny florescent tube light) as a backlight, unlike LED's these things aren't that rugged and can easily be broken by a shock from a sudden jolt, like a really bad fall from your table to a concrete floor.
After reading notes on different forums, I stumbled upon bad news. They said that if your backlight went dead, you'd have to replace the whole LCD, the backlight is fixed on the LCD assmbly and is non replaceable.
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