assuming that software you purchsed is in the form of a DLL...
When the user clicks "submit" to send the contents of the form, the .asp page should simply add the contents of that form into a table in your sql 2005.
Create a trigger in sql 2005 "on insert" to run the dll using this method:
It basically becomes a "job" that SQL will take care of.
We did something similar once at a place I worked, we use SQL to run an ftp dll for our web publishing. The request would be put in through a form, the site id would be sent to a db table an the sql would execute the ftp com object in the backgroud.
The user could close their browser window even log or turn off their machine and it would continue as normal...
There is a bit of a learning curve, you can search for "execute a dll from sql" for more/better examples, but once you get the hang of it, it's pretty easy to implement.
Another option would be to do the processing in a pop-up window and using javascript to close that window once the processing is complete (onload) -> be sure to include a message on the screen that says something like "your request is being processed, do not close this window, it will close automatically"
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GOOGLE is a great resource to find answers to questions like "how do i..."
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