How do i test my remote sql server connection?

If you just want to test connection's to the port/ip of the server/machine you could try the command line
telnet ip.of.sql.server port

50cal.

from the command prompt:

OSQL -S SERVERNAME -U USERNAME -p password

or
 (if you using intergrated security to connect to sql server)

OSQL - S SERVERNAME - E

Here is a tool which i found on a Dell Management Console CD. You can test for anykind of connection you like. IT will work with SQL and much more. it is called troubleshoot.msi. IT is a general tool to troupleshooot any kind of connection issue. you have to rename the file from .PDF to MSI. It work very well and DELL also has great support.