I'm having this same problem. Here's my log file (from uninstallation through reinstallation and application install attempt):
[2012-04-26:15:51:49] Runtime Installer begin with version 3.2.0.2070 on Windows 7 x86
[2012-04-26:15:51:49] Commandline is: -uninstall
[2012-04-26:15:51:49] Installed runtime (3.2.0.2070) located at c:\Program Files\Common Files\Adobe AIR
[2012-04-26:15:51:49] Starting runtime uninstall. Uninstalling runtime version 3.2.0.2070
[2012-04-26:15:51:49] Uninstalling product with GUID {47FA2C44-D148-4DBC-AF60-B91934AA4842}
[2012-04-26:15:51:51] Runtime Installer end with exit code 0
[2012-04-26:15:52:58] Runtime Installer begin with version 3.2.0.2070 on Windows 7 x86
[2012-04-26:15:52:58] Commandline is:
[2012-04-26:15:52:58] No installed runtime detected
[2012-04-26:15:53:01] Relaunching with elevation
[2012-04-26:15:53:01] Launching subprocess with commandline c:\users\u374441\appdata\local\temp\aire999.tmp\adobe air installer.exe -ei
[2012-04-26:15:53:01] Runtime Installer begin with version 3.2.0.2070 on Windows 7 x86
[2012-04-26:15:53:01] Commandline is: -stdio \\.\pipe\AIR_7984_0 -ei
[2012-04-26:15:53:01] No installed runtime detected
[2012-04-26:15:53:01] Starting silent runtime install. Installing runtime version 3.2.0.2070
[2012-04-26:15:53:01] Installing msi at c:\users\u374441\appdata\local\temp\aire999.tmp\setup.msi with guid {47FA2C44-D148-4DBC-AF60-B91934AA4842}
[2012-04-26:15:53:03] Runtime Installer end with exit code 0
[2012-04-26:15:53:04] Elevated install completed
[2012-04-26:15:55:57] Application Installer begin with version 3.2.0.2070 on Windows 7 x86
[2012-04-26:15:55:57] Commandline is: C:\Users\u374441\Downloads\RealityChartingV6.0.air
[2012-04-26:15:55:57] Installed runtime (3.2.0.2070) located at c:\Program Files\Common Files\Adobe AIR
Could you guys try creating a new, temporary, administrator account and see if AIR will install with the new account?