It's hard to tell from that picture. Are the leaves that are yellow on the canes (stems) that had berries? Have you already picked the berries this year? If so, this is the normal process. The canes die after fruiting. The new canes that are growing and are green this year will fruit next year and then die. After they fruit and start dying, you should just cut them out. Be careful not to cut out the canes that haven't fruited and are green. They'll fruit next year. If you cut them out, you'll have no crop next year. See the link below.

Here is a link that might be useful: Pruning Erect Blackberries

Can't tell from the photo, but it looks like a small patch of ground was cleared for the original planting, and now the grass is creeping back in. That much grass that close to the blackberry will compete for water.

Cannot tell from the picture or your text if the plant has had enough water or not. The whole thing is quite a jumble.

I would give up on the dead portions and prune them out. Leave the green leafy portions; they may start quite low. Clear the ground at least a foot in all directions from the canes, grass roots and all. Get a couple of green metal field T-stakes and place them a couple of feet away on each side of the canes, run some wire or cord to keep the canes upright between the stakes. The support you have now will not be adequate if the plant does become healthy in future years.

Unlike raspberries, blackberries don't mind damp ground all summer long. Probe the ground 4-6" deep on occasion to see how dry it is.

Add some composted manure around the plant in late fall or winter.