After several attempt to run slapd with TLS Cert, found somebody who told me: “…If you generated them using OpenSSL, you're going to run into problems. Debian switched over to using gnutls a while ago, and it doesn't play nice with OpenSSL certificates”…
Here are some details my syslog shows:
Sep 15 12:05:36 dec1 slapd: @(#) $OpenLDAP: slapd 2.4.11 (Jul 24 2010 08:14:20) $#012#011@murphy:/build/buildd-openldap_2.4.11-1+lenny2-i386-H5BDjb/openldap-2.4.11/debian/build/servers/slapd
Sep 15 12:05:37 dec1 slapd: main: TLS init def ctx failed: -1
Sep 15 12:05:37 dec1 slapd: slapd stopped.
Sep 15 12:05:37 dec1 slapd: connections_destroy: nothing to destroy.
So I am going to test generating the certs with gnutls certificate generator: certtool.
By the way does anybody knows how to install the Python-certtool?