Even though the SQL Server is installed on D: the default location of the databases

seems to be set to C:, so its looking in 'C:\Program Files\Microsoft SQL
Server\MSSQL\data\ folder for model.mdf' and modellog.ldf. You would have to make
sure that these are in the right location for the server to start.

Otherwise you can start the server from command prompt by

sqlservr -c -T3608

This will prevent recovery of all databases except model.

Usually the resolution is to rebuild the master databases

To rebuild the master database 1. Shutdown SQL Server; then run Rebuildm.exe in the
Program Files\Microsoft SQL Server\ MSSQL\ Binn directory. 2. Click Browse. 3. Select
the \Data folder on the Microsoft? SQL Server? compact disc or in the shared network
directory from which SQL Server was installed; then click OK. 4. Click Settings.
Verify or change the character set, sort order, and Unicode collation used for the
master database and all other databases. 5. The default character set, sort order,
and Unicode collation are shown initially, which may not be the values selected
during SQL Server Setup. You can select the same combination used earlier or select a
new combination; then click OK. 6. Click Rebuild. The Rebuild Master utility
reinstalls the master database.

In the process you can make sure the data folder is set to D

Later , after rebuilding master you will have to re-attach all the user databases
using sp_attach_db

You also will lose all the logins and will have to recreate them , and then relink
the database users using sp_change_users_login