Can't place any item from any inventory

If it's all of them, I don't think there is a solution.

Only thing that I can think of to try is using a mod. Can't really talk about it here but I can give you a clue where to look if you're willing to go down that road (at your own risk, this solution is not supported by EA)

Just read your sig - ignore that PM, then.

A hint would be helpful, if there's nothing else for it! Thanks.

Try either MasterController or ErrorTrap (use google to find them)

OK.

I just backed up my current game. Do you think, if I uninstall my game and reinstall it, would my saved family still have the same problem?

Try a new game first to see if that has the same issue. If not, reinstalling won't help since it's the game that has the issue.

Yep, new families have the same issue.

Are you able to tell me anything about how MasterController might help solve my problem? Perhaps if you specifically knew you would have said so, and perhaps you can't get into specifics, but thought I'd ask. I'm trying to find that out elsewhere.

Are you using other mods in your game ?

MC has a function to 'sort inventories' which usually unstucks stuff but I don't think this is going to help if even new games are affected by this issue.

Try the factory reset described in this post: http://answers.ea.com/t5/The-Sims-3/FAQ-Troubleshooting-Steps/td-p/714/

I downloaded an EA outfit and an empty Moonlight Falls neighborhood - would the latter be CC?

If not, does the factory reset only fix problems caused by CC? 

We did the factory reset and it has fixed the error. We must have done it slightly wrong as we weren't able to get my backup games working, but that isn't a tragedy. There's a certain excitement about starting again. I'm just relieved I didn't have to uninstall and reinstall everything.

Thanks for your help!