Ok, we got the reports working on our web-server. Thank you for the help.
The only issue is when client run report from browser he will get the window asking the password, see attached. After he types the password data is pulled from data base and everything is ok.
It looks it is ODBC issue as actual data base is located on different server.
When I remove the connection from "System DSN" report will not run at all .
Our developer has 2 ODBC set on his machine -"System DSN" and "User DSN". Everything is working fine on his PC.
As website is running under some virtual account IIS creates automatically I dont have option to create ODBC connection in "User DSN" for that account.
Actually I would like to avoid using ODBC connection at all.
I guess that some string needs to be added to aspx file which trigger rpt file or rpt file needs to be saved with proper connection to DB on developer PC.