Fix: Cannot Start SQL Server Service Error 3417

Detach you database. Overwrite the mdf and ldf files you've restored from your backup with your files from the D: drive. Reattach the database.
There is no guarantee that this will work or if it works, that your database is in a state where you can continue to work with.
If that doesn't work then there is an option to try to restore database using SQL Server Recovery Toolbox. It is a powerful tool for data recovery. They have a demo version. So you can check it works in your situation or not.
http://www.oemailrecovery.com/sql_repair.html

An MDF file isn't a backup file isn't the main data file (or master data file depending on who you ask) hence the file extension MDF. You can attach the MDF to the database by right clicking on the databases folder in Enterprise Manager (SQL 2000) or Management Studio (SQL 2005) then selecting all tasks and then Attach Database.
When you do this you will get an error about the log file missing. This shouldn't matter as SQL Server will simply create a new log file for you.
This will only work if the SQL Server was stopped when you copied the MDF file from the old SQL Server. If you copied the file while the SQL Server was running this file probably will not attach either and you will need to get a valid backup of the database.
Download help tool for sql database - SQL Server Restore Toolbox.
http://www.sqlserver.restoretools.com/
You can read up more on SQL Server here.
http://www.filerepairforum.com/forum/microsoft/microsoft-aa/sql-server/498-creating-a-new-database-using-an-mdf-file?_=1416149856104/

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.

You have a named instance installed with dynamic ports configured (default) named "local". In this case, the connection string would be localhost\local instead of local:1433. You could alternatively configure the service to use a fixed port and then connect using just localhost:. With dynamic ports, you would have to resolve the name of the service through SqlBrowser, which should be running

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.