For one, you dont want a steam server on a separate computer, you want hlds.
Here is an example of mine, or 1 of em at least:
C:\serverdoc\serverdoc.exe c:\HLServer_beta\hlds.exe -console -game cstrike +ip 192.168.1.98 -port 27015 +secure +maxplayers 14 +map de_dust2 +fps_max 600
In your case you can have it pointing to; (and of course change what you need changed, like ip, maxplayers and yada yada, self explanatory.
C:\serverdoc\serverdoc.exe C:\program\steam\steamapps\myname\dedicated server\hlds.exe -console -game cstrike +ip 192.168.1.98 -port 27015 +secure +maxplayers 14 +map de_dust2 +fps_max 600
I would highly recommend not using a steam server, it sux if you want a more legit server.
Just dl hldsupdatetool.exe and put that in your HLServer dir, then follow the dir that come with with it in the txt file. Its just a simple dl after a command line.