Permissions on Apache; 403

Inherited this machine, Linux this.machine 2.4.21-27.0.2.TL #1 Wed Jan 19
12:57:28 EST 2005 i686 athlon i386 GNU/Linux.

Now I don't seem to be able to get new users into publishing via
public_html.
It is possible to create the accounts, add the public_html. But whatever I
do, I get stuck with 403, Forbidden. Even tried chmod -R 777, as root, but
it stays like this. So it can't be a problem to the current user.
The error log says:
(13)Permission denied: access to /~mydir denied.
For the existing hundred-and-something users everything is okay.

I googled for some time, but didn't get further yet.

Uwe