I'd agree with what the others have said. Clean the droppings gently away from her vent and dry it. Check for any sores there and dress with antibiotic ointment. You'll want to remove droppings clinging to her vent daily or you might end up with maggots there. Seriously. Flies love that nasty stuff.
Second, we need to help you determine WHY she has "pasty vent". Like the others asked, what exactly is she eating. (If a combination of pellets, grains, what percentage of each?) Does she only have access to waterer water at your place, or any ponds, puddles, etc? Is she free ranged, penned, etc? What exactly do her droppings look like? Solid with white urates on top with only a few pudding like droppings? Mosty pudding like? Green and runny, green and frothy or any bubbles, any yellow? Rusty or reddish? Any mucus?
Also, oddly, sometimes pasty vent comes from parasites. Check her very carefully - flashlights help this - against her skin for the nearly microscopic parasites and their eggs - particularly around the vent area. Parasites love the heat and moisture. Let us know if you see any.
Third, she'll need probiotics regardless. At this point, you could give yogurt with some crumbles. A wonderful recipe is 1 teaspoon of yogurt, a little applesauce, a little water, a little bit of egg yolk (save the rest in the fridge or freezer for later), and crumbles - mix together til it's not wet but wetter than usual. Feed her a little of that. instead of yogurt, you could use Probios of Fastrack from the feedstore. Or acidophilus capsules' contents purchased at the health food store, grocer, or pharmacy. In addition to the probiotic in the food, you *could* add organic apple cider vinegar in the water. I think this would be a good and cheap idea.
It'll help balance the pH in her total digestive tract, adds enzymes that help digest food, makes a good environment for good bacteria and unfriendly for bad bacteria, and will help any yeast inbalances in case she has that going on.
