Check the version of your SWF file. It needs to be SWF10. You might get SWF9.
1)Try Overlaying SDK to 2.0 like:
a)Download the AIR SDK 2.0 zip
b)and paste it at C:\Program Files\Adobe\Flex Builder 3\sdks\3.2.0 and
c)extract it.Check whether this SDK selected in Flex Compiler.
2) Make sure that you have changed the AIR version number in descripter file (-app.xml) for example
<application xmlns="http://ns.adobe.com/air/application/1.5"> here have to change 1.5 to 2.0.
3) In the Flex Compiler panel check that which Flex SDK (3.5) has been selected. Might it different from defaultly selected.
In Flex Builder you can check in two ways :
a)Window>Preferences>Flex>Installed SDKs(Default)>Check SDK selected.
b)Select Project folder in Navigator Panel and Mouse Right click >properties>Flex Compiler>Check SDK selected.
4)Make sure that the opening files have accessibility with this function.
I have verified all the things you have mentioned. The application descriptior has version 2.0 in namespace, compiler is set to use flex sdk 3.5.
Can you elaborate on what you mean by "opening files have accessibility with this function.".
I tried to publish the application using Flash builder4 with flex 3.5 sdk and the application works fine.
I got the success after after targetting the flash swf to version 10 by changing htmlPlayerVersion="10.0.0" in .actionScriptProperties.
To set the AIR project in Flex Buildeder3 refer http://kb2.adobe.com/cps/495/cpsid_49532.html, there si a note at the bottom of the page for Flex Builder users.