I think that somehow when she was a puppy something bad happened around feeding time. For example, maybe she (and her littermates) were fed with one big bowl along with many other dogs of all ages (meaning that the feeding time was basically done like "slopping the pigs" and everyone was on their own to compete for the food. As you know, she is not much of a competitor, so possibly the other dogs acted aggressively with her (and among themselves) around feeding time). She may have been fine for a while, since when she was adopted by you the feeding scenario was different (and calmer and safer). It's a possibility that something relatively benign happened while she was eating to trigger the old anxiety again - sort of like having flashbacks. That benign something that could have triggered the psychological issue could have been some loud noise that happened just as she started to eat, a dog barking outside just as she started to eat, or the food bowl sliding on the floor and making a noise. You will never know what could have triggered it (and you will never know the story about how she became scared in the first place - it could have been something as simple as a large metal puppy bowl accidentally being knocked off of the counter while her breeder was preparing the food for the puppys - so it may have not even been a negligent (or abusive) scenario like the first one, it may have merely been an accident).
Certain dogs are basically genetically predisposed to not be as brave and confident as others. So, besides the unknown scenario that could have happened in her past, her genetics could be working against her. I even think that this could be a deeper thing than merely the food bowl - I think it could practically be the whole process of eating that is triggering a bad emotion due to something that occurred in the past during feeding time.
I would suggest doing anything with her that might build her everyday confidence. Training would be good as long as no corrections are involved. To find a positive motivation dog trainer in your area go to http://www.personalizeddogtraining.com/ and click on the Puppy Manners button and then in the index, click on Find a Trainer and that will take you to links where you can search for a trainer by your zip code. Before hiring a trainer or attending a class make sure that they train using positive motivation instead of correction (it's always best to sit in on a class prior to signing up to make sure you like what you see). Teaching her to do agility obstacles is also good.
Leadership exercises would also be a good thing to do to build her confidence. The NILIF (nothing in life is free) program is recommended. This is a life-long program, it will not work as a quick fix. The following web site explains the NILIF program in great detail! http://www.blackacorndogs.com/train_nilif.html
I also think that upping her exercise is necessary. The kind of exercise is the type that Cesar Milan recommends (not the treadmill part of his show) but the walks that represent a 'pack' migration. This means taking her on meaningful, we are really going somewhere, walks. No meandering, stopping and going, pausing and sniffing. The type of walk where you are taking the attitude that you are actually going somewhere important.
In additional to the confidence-building training, everyday routines, and exercise, veterinary behavior medications may also help her "get over the hump". I would not use these meds to try to get a quick fix. I would use them along with behavioral work to help her along. Then as the behavioral work progresses, the meds can be gradually weaned off.
I would probably choose another food instead of science diet. I would actually recommend doing the research and learning how to cook a balanced diet for her or learning how to prepare a balanced raw diet for her. I'm no nutritional expert, so I will refer you to my web site and the links on my web site http://www.personalizeddogtraining.com/webpages/dog%20food%20information.htm#Raw%20diets (you can actually buy balanced raw diets commercially). You can also buy some high calorie supplements to add to the food. I'm thinking along the line of a product called "STAT" - a high caloric liquid diet that can be used to supplement other foods. It is available at http://www.kvvet.com/.
I would totally change her feeding scenario. For now, feed her in a different location, on a different floor surface (you can buy some cheap carpet remnant and roll it out to protect your real carpet), not in a dish (try using paper plates). Also, get a different bowl for her water - try a square Tupperware-type of container so it is nothing like her old one. Also, change your routine of how you feed her. I.e. prepare it in a different location, do not say the same words you used to say, store the food in a new area, etc. This will not narrow down what was bothering her, since that is not what we are trying to do. Instead of caring what was bothering her, we are trying to build her confidence to eat again.
When you feed her, give her around 15 minutes and then pick the food up for 15 or 20 minutes before offering it again for 15 minutes. Do not keep adding new things to make her like it (that is, do not do this after offering it one way the first time). We do not want to teach her that if she waits you out she will get something else better added to her food.
There are also homeopathic medications, etc that can help with anxiety. You could go to a homeopathic veterinarian and see what they recommend, or you could try some things to see if they work (if she is on any prescription meds, please check with your veterinarian first).
There is a device called the Comfort Zone. The Comfort Zone relieves stress in cats and dogs by simulating naturally occurring pheromones that calm and reassure them in stressful situations. The Comfort Zone is a plug-in unit that releases D.A.P. (Dog Appeasing Pheromone) that mimics a natural reassuring pheromone produced by female dogs when nursing. I've heard some trainers say that they have had some successes with this. You could plug the Comfort Zone in in the room where you have decided to feed her. I recommend using a very quiet, enclosed area to feed her in.
There is also a dog calming device called "The Anxiety Wrap". This aids an animal's ability to focus, remain calm, and feel more secure.
If noise could be part of the issue, here is a site that sells doggy earmuffs to muffle out noise: http://www.safeandsoundpets.com/index.html
Here is another great web site concerning anxiety (probably focuses on thunderstorm anxiety, but may be of help to you also): http://www.adogslife.com.au/thunder.htm
Also, there are some homeopathics that can help with stress and fear. For example, BACH Rescue Remedy, Chill Out aromatherapy, Tranquil Anxiety and Stress Control, Nerve Ease, Homeopet Anxiety remedy, etc. Check out KV vet supply for the Comfort Zone, The Anxiety Wrap, and homeopathics (http://www.kvvet.com/)
Also, check out the book "The Cautious Canine - How to Help Dogs Conquer Their Fears" by Patricia B. McConnell, Ph.D. There are links to doggy book store sites from my web site http://www.personalizeddogtraining.com/ - click on the doggy marketplace in the upper left corner.
Hope this helps you get your dog to eat. You sound like a great pet owner. She is very lucky to have you.