I found about a dozen questions like this, read them all, but still can't find the problem.
I have a dedicated server running SQL Server 2008 R2 express. I enabled TCP/IP, added firewall exceptions, enabled mixed authentication, started SQL Browser.
I can connect to this database server from my home computer.
But from my work computer, I can't. I can, however, connect to RDP, I can telnet 1433 and get a response. I tried connecting from work to another sql server 2008 r2 and worked.