My MacBook Air screen stays white however the mouse works

Hello Openroad78,
I understand that when you boot up your MacBook Air, you see a white screen but notice that you can move your mouse. Let's see if we can get that sorted out.
I would start with using the troubleshooting outlined below. Start with booting your Mac into Safe Mode to see if you can access your information. If it works, then simply restarting your Mac will go through the normal startup process.
If it continues, you will want to use Disk Utility or fsck to check the status of your hard drive. Either option does the same exact thing, it is just how you start your Mac will determine which one you do. If you can get to your Recovery HD to access Disk Utility without getting a white screen, then that will be the route you take. If you still get a white screen you will want to boot to Single User mode to use fsck.
Resolve startup issues and perform disk maintenance with Disk Utility and fsck
https://support.apple.com/en-us/HT203176

Try Safe Mode

If you're using Mac OS X 10.2 or later, you can start up your computer in Safe Mode, which includes an automatic disk check and repair. If you're using Mac OS X 10.1.5 or earlier, skip to the next section. A Safe Boot, which starts up your computer into Safe Mode, might allow you to start up your computer successfully. To do this, follow these steps:

1. Start up in Safe Mode.
2. After the system has fully started up, restart your computer again normally.

If your Mac successfully restarts, the issue should be resolved. If the issue continues, try using Disk Utility.

Try Disk Utility

Use these steps to use the Disk Utility app to verify or repair a disk.

1. If you're using OS X Lion or later, start the computer from Recovery System or Internet Recovery. If you're using an older version of OS X and your computer came with a Mac OS X Install disc, insert the installation disc and restart the computer while holding the C key instead.
2. When your computer finishes starting up, choose Disk Utility from the Utilities window, or from the Installer menu if you're started from an installation disc.
3. Click the First Aid tab.
4. Click the disclosure triangle to the left of the hard drive icon to display the names of your hard disk volumes and partitions.
5. Select your Startup Disk (usually named "Macintosh HD").
6. Click Repair. Disk Utility checks and repairs the disk.

Tip: With Mac OS X v10.6 and earlier, always start up your computer from an Install or Restore disc when using Disk Utility to verify or repair your startup volume. Otherwise, you might see some disk error messages.

Use fsck if necessary

The command-line utility fsck can also be used to verify and repair a disk. If you can successfully start up in Safe Mode or use Disk Utility while started up from a disc, you don't need to use fsck. Here are some situations in which fsck may be necessary.

• Your Mac can't be started from the Recovery System or Internet Recovery.
• Your Mac OS X disc isn't available.
• Your optical drive isn't available.
• You can't start with a Safe Boot by holding the Shift key during start up.

Tip: If you use a Mac OS X Extended (Journaled) formatted volume, such as with Mac OS X 10.3 or later, you probably don't need to use fsck. If you do use it for any reason, please be aware that benign error messages can appear.

If you're not sure how your volume is formatted and you can't start up from your Mac OS X volume to find out, type the following command in a command-line interface and then press Return:

diskutil info /

If you see "File System: Journaled HFS+" returned, you have a Journaled volume.

To use fsck, you must use it from the command line. Unlike using your pointer to open an application to do something, you'll need to type a text command at the prompt (#) to tell fsck what to do. The Terminal application (/Applications/Utilities) and single-user mode are two examples of command-line interfaces where you can type these kinds of commands. To use fsck:

1. Start up your computer in single-user mode to reach the command line.
   
   Note: If your computer is unresponsive, force it to power off by holding down the power button for several seconds. Then press the power button again to start up the computer.
   
2. At the command-line prompt type:
   
   

   /sbin/fsck -fy

   
   
   Press Return. fsck will go through five "phases" and then return information about your disk's use. Once it finishes, it'll display this message if no issue is found:
   
   

   ** The volume (name_of_volume) appears to be OK

   
   
   If fsck finds issues and alters, repairs, or fixes anything, it displays this message:
   
   

   ***** FILE SYSTEM WAS MODIFIED *****

   
   
   If this message appears, repeat the fsck command you typed in step 2 until fsck tells you that your volume appears to be OK (first-pass repairs may uncover additional issues, so this is a normal thing to do).
   
3. When fsck reports that your volume is OK, type

   reboot

   at the prompt and then press Return.

Your computer should now start up normally and allow you to log in.

Take care