Group selection Tool doesn't work

If the objects within a group that you are trying to select have no fill then you must be sure to do your Group Selection Tool clicking on the stroke or nothing, indeed, will happen. If there is a fill in the objects and you're clicking and nothing happens then you may need to trash your Illustrator preferences.

To do so:

For Macintosh Users: With Illustrator closed launch a Finder Window in column view and click on your home folder. With the Option Key pressed choose Library from the Finder Go Menu. Within the Library folder find the folder called Preferences and within it find the following two files and delete them: “Adobe Illustrator <Version #> Settings” (earlier versions of Illustrator might just say “Adobe Illustrator”) and “com.adobe.Illustrator.plist”. When Illustrator is next launched it will create new preference files and the program will be restored to its defaults.

For Windows Users: On Windows 7 and above the preference files are hidden. To find them go to the Control Panel and open Folder Options and then click the View tab. Then select “Show hidden files and folders” or “Show hidden files, folders or drive options” in Advanced Settings. Then delete (or rename) the folder at the end of this path: C:\Users\[User Name]\AppData\Roaming\Adobe\Adobe Illustrator [version number]\ Settings\<Language>. Make sure that Illustrator is closed when you do this. When you relaunch the program it will create  new preference files and the program will be at its default settings.

After you’ve reset up the program (make sure that no document window is open) to your liking, it is a really good idea to create copies of your personalized “mint” preference files (make sure that you quit the program before copying them—that finalizes your customization) and use them in the future to replace any corrupt versions you may need to delete.