Here is a few steps to make sure Google Drive for the Desktop is working and how to turn it back on.
First, let go ahead open up the app incase it didn't open up when you signed in:
1: Hit the Windows key on the keyboard or on the screen
3. Open the app
4. Once it may prompt you to sign in again, if so follow the steps and you're all set! If not, check out the next steps.
If you open it back up and the G: still have a question mark follow these steps to access the share again:
1. Click the ^ on the task bar, for most this will be the bottom right of your screen.
2. Is the Google Drive icon grey? If so, click it to open it up.
3. If you see you email/Google account click the settings cog wheel.
4. Click Resume syncing.
Your Drive icon in the taskbar should now be colored in and you should be able to access the G: shares again!