Error: The Web application at http://...sitename.../ could not be - Ax

Hello all,

I have the following problem. I wrote the web application using ASP.NET
using SharePoint model. Everything looked good and worked fine when I tested
the application using the administrator account. Then when I put the web
application live and tested it using regular user account the application is
not working and throw following error right at the begining:

The Web application at http://...sitename.../ could not be found. Verify
that you have typed the URL correctly. If the URL should be serving existing
content, the system administrator may need to add a new request URL mapping
to the intended application.

The code that throws this error looks like following:

SPSite siteCollection = new SPSite("http://...sitename...");

I can see the Sharepoint website http://...sitename... normaly in Explorer
using the same account. Obviously it is some problem with the access rights.
I googled the web and find a lot of suggestions. For example the fololowing
ones:

http://support.microsoft.com/?kbid=832816
http://forums.microsoft.com/TechNet/ShowPost.aspx?PostID=1125480&SiteID=17
http://forums.microsoft.com/TechNet/ShowPost.aspx?PostID=1125480&SiteID=17
http://jack.whyyoung.com/tags/MOSS-Problem-web-application-object-mode.htm
http://www.kbalertz.com/kb_935751.aspx
https://forums.microsoft.com/MSDN/ShowPost.aspx?PostID=726395&SiteID=1
http://www.microsoft.com/technet/community/newsgroups/dgbrowser/en-us/default.mspx?dg=microsoft.public.sharepoint.development_and_programming&tid=73f12d49-07d4-4282-99ac-140110255bba&cat=en-us-technet-sharepoint&lang=en&cr=US&sloc=en-us&m=1&p=1

I followd all the instructions there but nothing helped. I used the same
applicatipn pool ID for website, created new one with different access
rights, added access for account ASPNET and NETWORK SERVICES for sharepoint
site and in SQL server, but no success - same error over and over. I am
already desparate. Intiristing is that if I log to the computer with
administrator account and then log to sharepoint as regular user it works
fine. However as soon as I log to the computer as regular user, the error is
there again. I do not understand it at all, I thought web application runs on
the server and IIS is taking care of access rights no matter how I am logged
to the computer.

What I have also found is that if I add user group Domain Users in WSS
Central Administration to the list Central Adminstration -> Application
Mangement -> Policy For web application  and give it the right to "read all"
(only option regarding reading there) then it works and the error is not
there anymore. However Sharepoint then starts to ignore lower access right
specified on lists,  document libraries and folders and users can see and
browse everything on sharepoint site regardless the settings in sharepoint.
So this is not accaptable solution for me. However I cannot specify in
Central Adminstration -> Application Mangement -> Policy For web application
to see only something.

Does anybody has any idea how to solve this? Any help would be highly
appreciated.

Thanks for any info in advance.

Roman