失礼しました
インストールしようとするとこんな感じです
# apt-get install dovecot-common dovecot-imapd dovecot-pop3d
Reading package lists... Done
Building dependency tree
Reading state information... Done
The following NEW packages will be installed:
  dovecot-common dovecot-imapd dovecot-pop3d
0 upgraded, 3 newly installed, 0 to remove and 0 not upgraded.
Need to get 0B/2922kB of archives.
After this operation, 5853kB of additional disk space will be used.
Selecting previously deselected package dovecot-common.
(Reading database ... 38056 files and directories currently installed.)
Unpacking dovecot-common (from .../dovecot-common_1%3a1.0.10-1ubuntu5_i386.deb) ...
Selecting previously deselected package dovecot-imapd.
Unpacking dovecot-imapd (from .../dovecot-imapd_1%3a1.0.10-1ubuntu5_i386.deb) ...
Selecting previously deselected package dovecot-pop3d.
Unpacking dovecot-pop3d (from .../dovecot-pop3d_1%3a1.0.10-1ubuntu5_i386.deb) ...
Setting up dovecot-common (1:1.0.10-1ubuntu5) ...
Not replacing deleted config file /etc/dovecot/dovecot.conf
Not replacing deleted config file /etc/dovecot/dovecot-ldap.conf
Not replacing deleted config file /etc/dovecot/dovecot-sql.conf
grep: /etc/dovecot/dovecot.conf: No such file or directory
grep: /etc/dovecot/dovecot.conf: No such file or directory
You already have ssl certs for dovecot.
invoke-rc.d: initscript dovecot, action "start" failed.
dpkg: error processing dovecot-common (--configure):
subprocess post-installation script returned error exit status 1
dpkg: dependency problems prevent configuration of dovecot-imapd:
dovecot-imapd depends on dovecot-common (= 1:1.0.10-1ubuntu5); however:
  Package dovecot-common is not configured yet.
dpkg: error processing dovecot-imapd (--configure):
dependency problems - leaving unconfigured
dpkg: dependency problems prevent configuration of dovecot-pop3d:
dovecot-pop3d depends on dovecot-common (= 1:1.0.10-1ubuntu5); however:
  Package dovecot-common is not configured yet.
dpkg: error processing dovecot-pop3d (--configure):
dependency problems - leaving unconfigured
Errors were encountered while processing:
dovecot-common
dovecot-imapd
dovecot-pop3d
E: Sub-process /usr/bin/dpkg returned an error code (1)

お解りの方いらっしゃいましたらよろしくお願いいたします

ありがとうございます
実行してみました　結果を貼り付けますのでアドバイスのほどよろしくお願い致します。

#apt-get purge dovecot-common dovecot-imapd dovecot-pop3d
Reading package lists... Done
Building dependency tree
Reading state information... Done
The following packages will be REMOVED:
  dovecot-common* dovecot-imapd* dovecot-pop3d*
0 upgraded, 0 newly installed, 3 to remove and 0 not upgraded.
3 not fully installed or removed.
After this operation, 5853kB disk space will be freed.
Do you want to continue [Y/n]? y
(Reading database ... 38297 files and directories currently installed.)
Removing dovecot-pop3d ...
Can't open /etc/dovecot/dovecot.conf: No such file or directory.
invoke-rc.d: initscript dovecot, action "start" failed.
dpkg: error processing dovecot-pop3d (--purge):
subprocess post-removal script returned error exit status 1
Removing dovecot-imapd ...
Can't open /etc/dovecot/dovecot.conf: No such file or directory.
invoke-rc.d: initscript dovecot, action "start" failed.
dpkg: error processing dovecot-imapd (--purge):
subprocess post-removal script returned error exit status 1
Removing dovecot-common ...
invoke-rc.d: initscript dovecot, action "stop" failed.
dpkg: error processing dovecot-common (--purge):
subprocess pre-removal script returned error exit status 1
invoke-rc.d: initscript dovecot, action "start" failed.
dpkg: error while cleaning up:
subprocess post-installation script returned error exit status 1
Errors were encountered while processing:
dovecot-pop3d
dovecot-imapd
dovecot-common
E: Sub-process /usr/bin/dpkg returned an error code (1)

気になったのですが、

>#/ver/lib/dpkg/info/ の中の
>dovecot-pop3d
>dovecot-imapd
>dovecot-common
>を消して、下記をやると削除されたように見えるのですが。。。
を実施しているので、dpkgを壊してしまっているのではないでしょうか？
dpkg -l | grep dovecot
を実行してパッケージが表示されますか？

>再インストールしようとしたらcourier-imapない
aptitude search courier-imap
を実行すると、私の環境(8.04のServer版)では、パッケージが表示されました。

># dpkg -l | grep dovecot
>pF  dovecot-common                            1:1.0.10-1ubuntu5           >secure mail server that supports mbox and ma
>rHR dovecot-imapd                             1:1.0.10-1ubuntu5           >secure IMAP server that supports mbox and ma
>rHR dovecot-imapd                            1:1.0.10-1ubuntu5           >secure POP3 server that supports mbox and ma
→dovecot-imapd、dovecot-imapdがremove状態になっているの置き換えで失敗していると考えられます。(多分、内部ではinstallコマンドの実行だと思います)

debパッケージを直接ダウンロードしてきて
dpkg -i --force パッケージ名
を実行して強制インストールしてみてはいかがでしょうか。
その後は、apt-getでパージできると思います。

もしくは、エラーメッセージに表示される設定ファイルをすべて
touch <設定ファイル名>
chmod 666 <設定ファイル名>
などダミーファイルとして作成してはいかがでしょうか。
これならapt-getでインストール→パージできると思います。

私の環境では「source.list」は、以下のようになります。
deb http://archive.ubuntu.com/ubuntu/ hardy main restricted
deb-src http://archive.ubuntu.com/ubuntu/ hardy main restricted
deb http://archive.ubuntu.com/ubuntu/ hardy-updates main restricted
deb-src http://archive.ubuntu.com/ubuntu/ hardy-updates main restricted
deb http://archive.ubuntu.com/ubuntu/ hardy universe
deb-src http://archive.ubuntu.com/ubuntu/ hardy universe
deb http://archive.ubuntu.com/ubuntu/ hardy-updates universe
deb-src http://archive.ubuntu.com/ubuntu/ hardy-updates universe
deb http://archive.ubuntu.com/ubuntu/ hardy multiverse
deb-src http://archive.ubuntu.com/ubuntu/ hardy multiverse
deb http://archive.ubuntu.com/ubuntu/ hardy-updates multiverse
deb-src http://jp.archive.ubuntu.com/ubuntu/ hardy-updates multiverse
deb http://security.ubuntu.com/ubuntu hardy-security main restricted
deb-src http://security.ubuntu.com/ubuntu hardy-security main restricted
deb http://security.ubuntu.com/ubuntu hardy-security universe
deb-src http://security.ubuntu.com/ubuntu hardy-security universe
deb http://security.ubuntu.com/ubuntu hardy-security multiverse
deb-src http://security.ubuntu.com/ubuntu hardy-security multiverse