Thanks for the advice. Since I posted this originally I have done a ton of research, and it looks like my problem lies with my web server not being trusted for delegation.

My application can access my web services on my web server, but my web server cannot access my database on my database server. From the reasearch I have done, I can impersonate myself on my web server, but I can only access local stuff on my web server as my impersonated user.

This is getting to be some heavy, confusing stuff, but I think I am on the right track to a resolution.