Could you please attach a DXDiag report for your system? What version of After Effects are you using?
3rd Party Sites:
Have you seen the performance tweaks on the Adobe site? Improve performance
And finally, this is a good source for configuring After Effects. Setting Up After Effects for Optimum Performance with 64-Bit Systems - After Effects Tutorial
Thank you for taking some time to help me out.
Here is the result of the DXDiag program: (I cannot attach a .txt file to this reply so I post the content of the file in here.
Hopefully you can see something in there which may cause this problem.
The version of After Effects is CC2014 (latest version - fresh install since last week).
I will also check the pointers you have put in your email