The machine where the sql sever is installed , there u gave the user name and password (unlike the window authentication)for ur sql server, Now check out ur connectionstring.I think , u did not mention the user name and passwod there. and on more thing , I think , the window authentication mode on the machine where the vs.net is installed has nothing to do withe the sql server(on another machine). so write the connectiionstring , keeping in mind the configuration of that machine where the sql server is installed.)
If you have an apple & I have an apple and we exchange our apples, then each of us will still have only one apple but if you have an idea & I have an idea and we exchange our ideas, then each of us will have two ideas!