Flip the leaves over. Are there tiny bugs on any? To me this looks most like damage from sucking insects like aphids.

Ariel, what zone are you in? That doesn't look like a grape that would do well in FL except maybe in 8b. Cluster grapes usually don't get enough cold here to bear. Have you had our heat wave up in the upper 90s and 100s? That's way too hot for most cluster grapes (another reason they don't grow here).

Has your neighbor sprayed weed killer around the fenceline lately? Grapes are very sensitive to weed killer.

Grape vines don't live forever. They will eventually die. Maybe this one is just very old and is on its last legs.

If I were you, I'd pull it all out and plant a nice muscadine or scuppernong vine that will give you some fruit.

I am in NYC. I belive zone 7.

I checked now and saw whiteflies under the leaves. Sprayed it with a hose and will put out a petroleum jelly traps later.

I also hosed down my other plants in case they spread there.

I don't think the vine is too old or weak. It never gave us any grapes since we planted it. No one took care of it or helped it climb on something to grow and get sun

I have checked it almost everyday and didn't see anymore whiteflies or any bugs on the leaves. The vine continues to grow new healthy vine and leaves. But the old leaves and clusters dry up. I have no idea why and think I should just pull it all out and start over with a new one but know which or where to get a new one that isn't expensive.

How do I select a new grape to grow? What is the best way to pull this one out?

You have a few fungal diseases there. You have to spray grapes every week or two depends on weather. I think you have mostly Black Spot there but possibly some other diseases.

I asked an extension and was told "That looks like anthracnose, which is a difficult to control fungal disease. Lime sulfur works okay against anthracnose, but your best bet is to plant a grape variety with some resistance to it. There are other fungicide products that work well against anthracnose, but most of them are only available for commercial production (large volumes and expensive) and you would need to spray regularly to prevent the disease. Anthracnose thrives under warm, moist conditions so it will probably be a recurring issue for you. It survives the winter on infected areas of the vine (the brown lesions) so if you keep your vine I would recommend pruning as much of the infection out as possible. "

I hate to cut down a vine and start over. I am leaning towards that though if its more cost efficient and easier to manage with a new vine. What fungicide would I use?

If you want to learn how to grow grapes and what to use and when, i would highly recommend to follow this blog

http://grapepathology.blogspot.com/

It is late for this year, so let it be. But you can start a proper management next year.