I solved this problem by adding the relevant lines to web.config:-
<section name="permissions" requirePermission="false" type="DotNetNuke.Framework.Providers.ProviderConfigurationHandler, DotNetNuke" />
<section name="moduleCaching" requirePermission="false" type="DotNetNuke.Framework.Providers.ProviderConfigurationHandler, DotNetNuke" />
<section name="outputCaching" requirePermission="false" type="DotNetNuke.Framework.Providers.ProviderConfigurationHandler, DotNetNuke" />
and:-
<moduleCaching defaultProvider="FileModuleCachingProvider">
<providers>
<clear />
<add name="FileModuleCachingProvider" type="DotNetNuke.Services.ModuleCache.FileProvider, DotNetNuke.Provider.ModuleCaching.FileProvider" providerPath="~\Providers\ModuleCachingProviders\FileModuleCachingProvider\" />
<add name="MemoryModuleCachingProvider" type="DotNetNuke.Services.ModuleCache.MemoryProvider, DotNetNuke.Provider.ModuleCaching.MemoryProvider" providerPath="~\Providers\ModuleCachingProviders\MemoryModuleCachingProvider\" />
</providers>
</moduleCaching>
<outputCaching defaultProvider="MemoryOutputCachingProvider">
<providers>
<clear />
</providers>
</outputCaching>
</dotnetnuke>
Also copied in the two dll's from the provider install zips into the bin/providers directory (renaming the existing ones).
Re-access the site, which will restart because web.config was edited, and all seems OK.
I have then re-installed the two providers via the interface, to make sure DNN knows what version is installe, etc. Install went OK this time.
It should be noted that I had PageBlaster installed on this site. That said it was also installed on my test site because I'd just done a fresh backup to my test site, so in theory it shouldn't be related to that.
Roger