If shes lost it totally, I would take her to the vet ASAP, shes too old to go very long without food. There could be a million things wrong with her. Is she still drinking water? Has her teeth ever been checked, at her age they could be really bad.
That's a good point. Plaque and build up of tartar on the teeth can cause sore gums, and that is one of the first things to stop a dog wanting to eat.
I also agree you should take her to be checked by a vet because there could be so many reasons why she's lost her appetite. The cause will need treating.
Have you noticed any other symptoms as well recently?
I agree with lindapalm about the vet check. If it should be the case that there is nothing identifiable or treatable wrong with her, I would just try to feed her the most appealing dog food that I could find. It is different with different dogs. There is no one thing that all elderly or sick dogs like.
Maybe she has always been fed kibble, but now she will only eat canned food. Or maybe she will eat kibble if you put some canned food on top of it to "dress" it and then run some hot water over it to soften the kibble and stir the whole concoction up. Maybe she will eat if you pour some milk over the top of her food. Maybe she likes spaghetti sauce, and she will eat if you put a little of that on top of whatever you are feeding her (be careful about too much tomato-y stuff, because it is acidic). My late dog liked this seasoning called Spike (Salt-Free), and she would eat better if I sprinkled that on her food.
Maybe you will have to feed her by hand. Some sick or elderly dogs will eat by hand when they won't eat out of a dish. Maybe she doesn't need to be hand-fed the whole meal, but she will need you to feed her the first few bites and sit with her while she eats. Maybe she needs her dish elevated (like, set on top of an overturned milk crate) instead of set on the floor. Maybe she needs to be fed more frequent, smaller meals than in the past. Maybe she needs you to cook for her more. White rice with some lean chicken and a few (just a few!) green beens in it is easy for most dogs to eat and digest; likewise scrambled eggs or white rice with scrambled eggs mixed in and a few green beans.
If she can tolerate more fat in her diet without getting loose stools or any other problems that you can see, then you can use a higher-fat dog food, or you can supplement fats (butter, olive oil, canola oil, whatever) to get more calories into her. Take it easy at first, and see how she does with this. If she was overweight in the past, and you were using a low-fat dog food, you probably don't need to do this anymore. There is a product called Dyne, which is basically soybean oil with vitamins in it, that you could try, to see if it will help her hold her weight. But again, start slow.
A 14 year-old Dal is like a little old lady in her 90's. You have taken good care of her, or she wouldn't have gotten to this point. Just use your ingenuity and your close knowledge of her to figure out what she would like and what feeding techniques will make it easier for her to take in what food she can.
Oh, there's one more thing. You could try putting some corn syrup on your finger and let her lick it off or just put it in her mouth, right before a meal. Do that three or four times, so she gets enough corn syrup in her to bring her blood sugar up a little bit, and see if it won't perk her up and stimulate her appetite so she will be interested in eating some regular food. There is a product calle Nutri-Cal, which is basically corn syrup with vitamins in it, and you can use that, if you can find it. But if you can't find Nutri-Cal, or if she doesn't like it, you can just use plain corn syrup or even honey. Don't overdo it; just use enough to whet her appetite and get her to eat her main diet.
When a dog loses appetite for more than a day or two, something is very much wrong. Loss of appetite in a dog as advanced in age as your Dally is something to be very concerned about. Don't wait and wonder - get to the vet as soon as possible!