I might be misunderstanding your question. You first say that you "want to only move a part of an object," so you select the point you want to move with the Direct Selection tool (white arrow). But then you say when you "try to move it, it only moves the one point you have clicked on instead of the entire object."
Is your goal to move a single part of an object, or to move the whole object?
I want to move all of the points that I have selected. But it will only move the part of the object that my mouse is over and deselect the others. Say I select 10 points on an object and then I try to drag them over an inch. I click on an area of the selected points and drag. But, it only moves one or so points and the others just sit there.
I've created a circle and added a couple anchor points to it. (3 points along the left side).
I select the first point, then shift+select the other two points, meaning three points are simultaneously selected.
I grab just one of the anchor points that I've selected and move them to the left and upwards.
I used the Direct Selection (white) arrow the whole time. My question is whether you are clicking and dragging an area near the points, or clicking one of the points and moving them?
Take a screenshot of your object and post it here, maybe there is something that I'm overlooking!
I am doing exactly what you are doing. I have done it for so many years that I am used to it behaving like it's supposed to. But something has changed and it wasn't me. I think there is some sort of preference that controls this that I messed up fiddling with things so when I go to drag the entire thing, whether I click on an anchor point or just the area of the anchor points, it will only select what my cursor has landed on. If it's an anchor point, it will only move that one anchor point, if it's not over one of the selected anchor points, it won't move anything. I have been trying to replicate it and can't seem to do it on this document. But some of my documents it does this and I can't remember which ones. Just that it is not the expected usual behavior.
Preferences > Selection & Anchor Point Display > Object Selection By Path Only
Make certain that is not checked. You may need to simply reset your preferences as well.
I don't have that selected but it's that quick type of fix I was hoping that is was. Something I checked or unchecked stupidly. Thank you anyway. Darn!
I was hoping not to have to do that since I have it all customized.
You may try to Move the folder: this is reversible so you can get your preferences back if resetting them fails to solve the issue.
Edit: I just saw that the link that Scott gave also includes renaming the preference file. If you do that, you may rerename it and get it back, remember to do it with Illy closed.
You can select the whole of an object using the Direct Selection tool and option-clicking on its path.
But as Scott suggests, your problem sounds as if you have checked 'Object Selection by Path Only' in Selection & Anchor Display prefs
Hmmmm....do you think it's possible that different files, perhaps ones I got from others, can have their preferences built in and be different from my own?
No. Preferences are not document specific, they are application wide.
But it is possible file from elsewhere contains an object which is constructed in a manner you aren't familiar with.