I like the first two words (glistening & glittering), as well as tchrist's shining.
Glittering might be especially apt if the dew was causing several individual points of light, as if glitter had been spread across the lawn.
I'm not so fond of glinting, perhaps because I often associate it with someone's eyes. NOAD lists this definition:
• (of a person's eyes) shine with a particular emotion : his eyes glinted angrily.
That said, the word's primary meaning is "give out or reflect small flashes of light," so it could be used in the dewy grass sentence.
Similarly, there's nothing wrong with gleam per se, but NOAD lists these definitions:
• (of a smooth surface or object) reflect light because well polished : Victor buffed the glass until it gleamed | [as adj] (gleaming) sleek and gleaming black limousines.
• (of an emotion or quality) appear or be expressed through the brightness of someone's eyes or expression : a hint of mischief gleaming in her eyes.
Since grass is not well-polished, and there are also more ties to eyes and emotions, I'd steer away from gleam as well.
As a general rule, it's worth examining secondary and tertiary definitions of words when trying to learn about how synonyms differ. Those additional meanings will sometimes – though not always – hold the keys to understanding why some words may sound a bit more out of place than others in certain contexts.
As for Martha's comments about pictures being worth a thousand words, that's another technique you can use. For example, I found these pictures using the Google image search:
I found these four images by typing (from top to bottom): "gleaming grass", "glinting grass", "glistening grass", and "glittering grass" into the Google image search bar. As you can see, the terms are largely interchangeable in this context. In fact, one of the pictures was captioned "magical atmosphere of the glittering and gleaming carpet in the grass," as if one adjective wasn't entirely sufficient.