How can I log in again after downgrading a 1st-gen MacBook Air from Lion to Snow Leopard? I have a 1st-gen MacBook Air. It came with, if I remember correctly, Leopard. I subsequently upgraded to Snow Leopard and then to Lion.

However, I have found it to be very sluggish after upgrading to Lion, so I decided to downgrade it to Snow Leopard.

Since doing so, I can no longer log in.

Here's what I did


Use SuperDuper! to make a bootable backup of my MacBook Air hard drive on a partition on an external USB hard drive
Boot using the aforementioned partition on external USB hard drive as startup disk to verify the clone. Verified.
On another Mac (one with a DVD drive), use SuperDuper! to clone the Mac OS X Snow Leopard install DVD onto another partition onto the same external USB hard drive.
On the MacBook Air, boot into the Install partition on the external drive.
Use Disk Utility to re-partition the MacBook Air's internal hard drive.
Install Mac OS X Snow Leopard on the MacBook Air's hard drive
When asked as part of the installation, choose to migrate users, applications and data from the other partition on the same external hard drive that contained the previously backed up hard drive
Restart the MacBook Air on successful installation
Attempt to log in with the password I originally had.


The login screen simply shakes its head at me and does not let me log in.

With my limited knowledge, I imagine that something has gone awry with password hashing. Any ideas what I can do?
You may want to try the method described here under 'Reset Mac Password – without a CD'. This method resets the OS so that it thinks that it's the first time it's been run. This will kick off the Create New User Account wizard when the OS is rebooted, which allows you to create a new account with Administrator rights. You can then use this account to reset the password of the original account.

Extract from above article:


  Stage 1) Boot into Single User Mode and remove a setup file
  
  
  Restart the Mac holding down the Command+S keys, this will take you
  into Single User Mode and it’s Terminal interface 
  You’ll need to check
  the filesystem first: fsck -fy
  Next, you must mount the root drive as writeable so that changes will
  save: mount -uw /
  Now, type the following command exactly, followed by the enter key: rm
  /var/db/.applesetupdone
  After removing the applesetupdone file, you need to reboot, type
  ‘reboot’ and hit enter.
  
  
  Stage 2) Create a New User Account upon System Boot 
  
  You aren’t finished, but the hard part is now over – no more
  command lines, you’ll now be in the familiar Mac OS X GUI to finish
  the password reset process. In this step we just create a new user
  account as if you just got a new Mac:
  
  
  Upon reboot, you will be presented with the traditional “Welcome
  Wizard” startup screen just like when you first get a Mac 
  Follow the
  welcome wizard and create a new user account – making the account name
  different from the account whose password you want to recover 
  Continue on and boot into Mac OS X with this newly created user account, this
  new user account is an Administrator and has administrative access
  
  
  Stage 3) Reset the Forgot Password via System Preferences 
  
  You are almost done, now you just need to reset the forgotten user account
  password using the Accounts control panel:
  
  
  Once you are booted into Mac OS X, click on the Apple logo and then
  navigate down to “System Preferences” 
  Click on the “Accounts” icon in
  System Preferences 
  Click on the Lock icon in the lower left corner of
  the “Accounts” preference window and enter the newly created user
  credentials, this enables you to change other user accounts and reset
  other users passwords 
  On the left side user panel, select the user
  account containing the forgotten password 
  With the user of the
  forgotten password account selected, click on the “Reset Password”
  button 
  Enter a new password for that user, be sure to include a
  meaningful hint so you don’t forget it again! 
  Close System Preferences
  and reboot the Mac 
  You can now login to the previously inaccessible
  user account using the newly reset password! All user files and
  settings are maintained as before the password was forgotten