OK, update. Hold on to your seat. I now have a basically operational iMac running Lion.
Problem was a bizarre one in the end, and it was only me uncovering the errors in my previous post that pointed Apple Support at the solution. All the disfunctional apps were Apple's own. The list included System Profiler, which gave me an error message when I opened it from the Utilities folder inside the Apps folder. The error message said I had a version for OS 10.6
The point is, there is no System Profiler app in Lion! It has been replaced with a utility called System Information, though confusingly this keeps the same icon. Upon devling into my folders and files, we found that Lion appeared to have installed a new, updated Applications folder, but had not put this on the Dock. The old one, containing pre-Lion software, was still on the dock.
Rebuilding the dock, deleting the former dock preferences, and relacing the Appls folder with the new one appears to have solved everything. Apple Support had no explanation for why or how this had happened, though.
I have been using Aperture through today, and it has worked just fine in all respects. Touch wood.