It won't pick up when I click with my mouse

Hello @FabulousApple, welcome to the forums. You are still able to click buttons in the menu and options menu right? So have you attempted to Reset Binds for the Controls in the Options Menu then try to play again? As far as I know there is no click+drag box that allows you to pickup items in DST unless you are using a mod. 

There is also another way to pick up items which is to press Spacebar (this is the default key bound to Do Action). Do Action will force your character to do the nearest action, so if there is an item on the ground they will pick it up.

Another thing you should probably check is if there are other peripherals interfering with your mouse clicks. Unplug any other inputs like controllers/etc and start up the game again. Since you mentioned batteries in your mouse, I'm guessing you are using a bluetooth mouse, try to unplug then replug the dongle that is partnered to your mouse.

Lastly, would you mind saying what operating system you are playing on?

In the mean time, try the things I mentioned first and report back if they worked or not.

Listing them down as follows:

• Reset Binds for controls
• Remove other input peripherals (game pad controllers, things that use usb ports etc.)

Good luck, cheers.

If there are any client mods installed, try disabling them and if it makes a difference.