Unable to add local server with SQL-Server Management Studio 2005

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upgrade it or
take backup of your database
install sql server 2008
Restore backup in sql server 2008

you cannot do that

Enable remote connections for SQL Server 2005 Express or SQL Server 2005 Developer Edition loadTOCNode(2, 'moreinformation'); You must enable remote connections for each instance of SQL Server 2005 that you want to connect to from a remote computer. To do this, follow these steps:

1. Click Start, point to Programs, point to Microsoft SQL Server 2005, point to Configuration Tools, and then click SQL Server Surface Area Configuration.
2. On the SQL Server 2005 Surface Area Configuration page, click Surface Area Configuration for Services and Connections.
3. On the Surface Area Configuration for Services and Connections page, expand Database Engine, click Remote Connections, click Local and remote connections, click the appropriate protocol to enable for your environment, and then click Apply.
   
   Note Click OK when you receive the following message:Changes to Connection Settings will not take effect until you restart the Database Engine service.
4. On the Surface Area Configuration for Services and Connections page, expand Database Engine, click Service, click Stop, wait until the MSSQLSERVER service stops, and then click Start to restart the MSSQLSERVER service.

there is facility in enterprise manager to take back of database!

First of all you need to be sure that when you installed sql server you also checked Database server. I assume you have.

Then you need to check if SQL is running.

You have to go to start and type services.msc in the search field.

then you have a list of services. go down to sql server and check if its running.

Now go to sql management studio and connect to your local server.

You also might have a instance name. like local server\sql express or an other name.

try to complete uninstall .net framework and install it again or get the latest copy of .net framework to install 3.5 latest version already available for download

Regarding what is .SDF -- A file format that is compliant with the combination of SQL Server 2005 Compact Edition, SQL Server 2005 and Visual Studio 2005 to build, test, deploy, and manage applications for users. Databases of this type can be accessed directly as a datasource, e.g., from Visual Studio 2005, or from SQL Server Management Studio. As such, they can be passed around with programs or projects, although they are mainly used for embedded applications. The file includes all necessary code points to access the data, and so does not require an instance of SQL Server to be installed.

You can create a .SDF file with a software called PocketSYNC. (Although i have never tried it myself, a lot of people claim that this software works like charm. But it is not free)

Two ways to access your server. First, make sure the SQL Server Service is running. Start | Run | Services.msc | Enter. Look for Microsoft SQL Server Service and that it's running. Or Look for the SQL Service Broker icon by the clock and see that it's running. The default instance of SQL Server uses the Hostname. Start | Run | Cmd | Enter. The type hostname. This will be the name to access to server. Then type IPCONFIG, this is then the IP address that you could also use to access it.

SQL Server runs on port 1433, so any firewall has to have it open.

Open Query Analyzer, type in the hostname or ip of the local box, type in "sa" and the password for sa (if setup in mixed mode) or Windows Authentication.

Once you login in, you should now see the databases in the Tree on the left side under the Server | Databases node.

Your description though states "SQL Server won't work on my laptop". TO answer this, the only two SQL Editions that work on anything other than "SERVER" software is SQL Professional and SQL Developer. All others have to be on a "SERVER" platform.