What version of ArcGIS are you using? What version of ArcSDE is running?
There are several different types of connections available from ArcGIS, only the "Database
Connections" tree element manages ArcSDE connections -- are you using this?
Is there a firewall running on the ArcSDE server host? If so, has the service port been
approved for communication from the client on that port?
Can you connect to ArcSDE from the ArcSDE server host?
- V