The normal steps for creating a new folder would be:
1) Click START
2) Click Computer
3) Right-click Documents, C:, or whatever folder you want the new folder in.
4) Point at NEW
5) Click FOLDER
6) Type new folder's name
Is that or something similar what you did? I've never seen Briefcase come up under these conditions. If you did follow these steps and somehow Briefcase came up, then you should boot to Safe Mode and check for viruses because this is certainly isn't normal.
If you do all the above and the problem still isn't resolved, then you should back up your data and restore to factory settings according to your computer's user guide (which should be on your hard drive).
I want to start a new folder in Windows Explorer, but the BRIEFCASE comes up instead of NEW. I can I correct this so I can open a new subfolder?