This problem does seem a bit random. Sometimes I can go in and edit pages fine, which are using the same template, and other times, more often than not, I get the problem I described.
When the problem does happen, one or both of the following script errors usually occur:
SCRIPT5007: Unable to set property 'control' of undefined or null reference
File: ScriptResource.axd, Line: 2713, Column: 13
SCRIPT5007: Unable to get property 'length' of undefined or null reference
File: ScriptResource.axd, Line: 857, Column: 1
However there are times when no script errors occur. Also, most of options in the top left of the screen aren't displayed; I'm just left with 'More actions' and 'Back to Pages', neither of which work, which means I have to click the browser back button then unlock the page.
Anyway, I have created a new page as you suggested, although oddly there aren't any built-in templates to choose from in this project so I have had to select start from scratch. I have gone into the page several times and I've been able to edit it every time without any problems. Can you tell me where I can get/install the standard built-in templates so I can rule them out?