I don't know if you can detach system databases, but you can try this:

1.  Shut down the SQL services

2. Copy the system ldf and mdf files

3. Install SQL Server to same version and service pack level

4. Stop SQL server

5. Rename new system databases

6. Put original system ldf and mdf in place of new files

7. Start up SQL.

I have used this technique with sucess during several server rebuilds.  It might work depending on what your disaster is.