Hi mdpemberton,
It sounds like your MacBook Air did not finish installing El Capitan. Is your MacBook Air connected to any peripherals (an external monitor, printer, USB hub, etc.)? If so, disconnect them before restarting. What happened when you started your computer in Safe Mode? Did it behave exactly the same way as you describe above?
If you are not getting past the grey screen, that means the computer can't find the startup (boot) disk.
About the screens you see when your Mac starts up
https://support.apple.com/en-us/HT204156
When you first turn on your Mac, the screen is off (black) and you hear a startup chime. Your Mac initializes its BootROM and memory (RAM). It then performs a power-on self test (POST) and a BootROM test. If you hear additional beeps or chimes at this point, this indicates a possible hardware issue and startup halts. If you've added memory to your Mac, check to make sure it's installed properly.
Blank screen

After the power-on self test is complete, your Mac sends a video signal to your connected displays. The display screen might appear black or gray at this point in the startup sequence and the display's backlight should turn on. If you don't see an image appear on your screen after a few moments, try turning up your display's brightness. If you're using an external display, make sure it's connected properly and turned on.
Apple logo

When you see the Apple logo appear, it means that the computer has found the startup file "boot.efi" on your startup disk. This tells your Mac where to locate the System folder on your startup disk.
OS X El Capitan: If you see a gray screen at startup
https://support.apple.com/kb/PH21899?viewlocale=en_US&locale=en_US
Use the built-in recovery disk to reinstall OS X while keeping your files and user settings intact.
Important: You must be connected to the Internet to reinstall OS X.
In the menu bar, choose Apple menu > Restart. As your Mac restarts, hold down the Command and R keys until the Mac OS X Utilities window appears.
Select Reinstall OS X, then click Continue.
Follow the onscreen instructions. In the pane where you select a disk, select your current OS X disk (in most cases, it’s the only one available).
Hope this helps.