Q: I was updating my laptop and now have a kernal error and cannot get anything to reinstall or start up properly.  I believe that I had a power outage when my mac air was in the middle of a software update and now I am stuck

You didn't have enough battery power left when performing the update, and it died? That's bad.

You should be able to reinstall OS X using OS X Recovery or in the case of an older MacBook Air running Snow Leopard, by using your original System Install DVD and Remote Install OS X from another Mac.

Reinstalling OS X does not erase your user accounts or data.

OS X Recovery:

http://support.apple.com/kb/HT4718

Remote Install OS X:

http://support.apple.com/kb/HT2129

That depends on the OS X version you were using. Try the second option first (OS X Recovery).

It seems the power loss resulted in a corrupted startup disk.

After you start OS X Recovery or Remote Install OS X, select Disk Utility from the Utilities window. Select your startup volume from the left column then Repair Disk. After it repairs the disk quit Disk Utility, which returns you to the Mac OS X Utilities window. Attempt to reinstall OS X again.

If this does not work it may be necessary to erase the internal disk. It is also possible that it has been damaged beyond repair. It can be replaced, if necessary.

What model MacBook Air do you have?

OK good, I wanted to make sure it was not an early one with a hard disk.

Try reparing the internal drive with Disk Utility.