Thanks Dan.
Unfortunately, this problem is back again! And I haven't even re-installed any third-party extensions. Which, as you might imagine, is very frustrating!
Things were working just fine, until I started trying to build a script in Python using Spatial Analyst functions (which was the same as last time). Now I can't run Spatial Analyst tools anywhere!
I'll try the normal templates approach again. I'm hoping that I won't have to un-install and re-install, again...