beta fish wont eat or swim; just floats at top of bowl

Question
I recently bought  betta fish for my children.(3 yr. old twins and a 5 year old)  Two of the fish are doing great.  they are absolutely beautiful and very interactive with me.  They get excited when i come close and fan out their fins and tail and follow my finger across the bowl.  

All 3 live in their own 1 gallon bowl with gravel and distilled water kept at room temperature.  ( i live in Florida)  The two healthy ones were healthy right from the start .  they immediately ate their food  (betta pellets)  i feed 2x a day 3 to 4 pellets.  I change their water once a week.

The sick betta was like this when i first brought him home.  He did not move much if at all.  and he would not eat ANYTHING for about 3 weeks.  I thought he would die.  Then,, one day I was making Mac n cheese for my kids and ,, accidentally I shook some of the cheese packet powder into the sick bettas bowl.  Well  all of a sudden, he started eating the cheese powder.  I then thought maybe he would prefer his betta food smashed into powder.  Yes,  he now ate the crushed betta pellets.  He started swimming and eating every day.  After about day 3 of crushed pellets , i tried a whole one and he gobbled it up.  So i fed him whole pellets from that day on and all was good.  He was now swimming happily like the other two and they were flaring all the time through their bowls.  The other two made bubble nests .  This one never did.

Ok , I think I dropped a few too many pellets one day accidentallhy ...about 10...so i scooped some out with a net.  When i change the water I take the fish out with a net and put himn into a small holding tank until his own bowl is clean.  with fresh water.  Maybe the net hurt his fins?  anyway, all of a sudden  ,now he is not eating at all.  is only floating at the top of the bowl and is never swimming.  never goes anywhere in the bowl but sits right at the top.  He does go up and move to get air.  I tried feeding the crushed betta pellets again but he would not even flinch.  The food actually touches floats to his body and he does not move.  I can tap the tank and he wont move.  He is basically listless.  Is he dying?  He has aready gone one week with no food.  he looks miserable.  I tried putting a light from a smalll fish tank on top of his bowl, but i am afraid of "frying "  the litte guy so I turned it off after a few hours.

I have reaad a ll the people who say a bowl is cruel.  But here, I have 2 out of 3 bettas with the same conditions who are doing great .  Beautiful and happy bettas with 1 gal. tanks and water change once a week and betta pellets.

My little girls are very upset about SCOOBY DOO...this will be their first lessen in death if he doesnt make it ..but I was hopin I could save him.  Any suggestions ...or does it sound llike its over for Scooby?

Answer
First of all, you need to stop using distilled water. It's pure, yes, but it has absolutely nothing in it. Including the minerals that occur naturally in your tap water that they NEED. Start using tap water with tap water conditioner (it takes out the harmful chlorine and chloramines). You can buy tap water conditioner at any store where they sell fish.
Since Scooby is stressed out, I suggest buying the kind of conditioner that adds slime coats to your fish as well, or aquarium salt and add a few grains each time you do a water change, to help prevent disease and reduce his stress. Aquarium salt (NOT marine salt) may be the better choice, since it will also put electrolytes back into the water.
Make sure his water is between 75-85 degrees F.
Try tempting him to eat using some thawed blood worms, most Bettas can't resist.