Mac won't show screen
If you have another device you could try a remote connection. Personally I would be tempted to SSH into the Macbook and see what processes are at play.

This will of course only work if you have 'remote login' enabled on your Mac.


  System Preferences > Sharing > Remote Login


From an iPhone you could then install an SSH client (search: ssh) from the App store and try connecting in.

After login you could try

$ ps -A |more


to list all processes currently running a page a time (space to advance)
or 

$ top


this will give you a list of processes (q to quit)