Getting computer info with Flash

I'm far from being an expert on this type of thing. My thoughts are conceptual only (possibly not sensible!) and I do not claim to be an expert in application security:

To do it in the way I think you want...I'm not sure how you could get enough local machine info to generate a very machine specific hash to use for the type of thing you are describing. The only way I see this being possible is via an extended API offered by a 3rd party tool. So the hash in the sharedObject is a combination of the machine information and something the server based validation does to it. The local app would recreate the machine based hash each startup and then compare it to the code in the sharedObject. The codes are not the same, but the check renders them as compatible, otherwise if not or if the sharedObject is not there, a server-based validation is required to regenerate the sharedObject data.

There's a limited amount of information available. I don't think you can directly get that information.

System capabilities offers this:
http://livedocs.adobe.com/flash/9.0/main/00001498.html#wp189495

Beyond that, if you are creating a projector style application, then you will be able to get more information if you use a 3rd party wrapper (depending on what the API of the wrapper exposes). E.g. Zinc, Swf studio and others (can't remember the names google for flash projector tools or something like that).