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Go to app/etc and find Mage_Newsletter.xml file. If it is not there open Mage_All.xml and find

<Mage_Newsletter>
    <active>true</active>
    <codePool>core</codePool>
    <depends>
        <Mage_Core/>
        <Mage_Customer/>
        <Mage_Eav/>
        <Mage_Widget/>
    </depends>
</Mage_Newsletter>

If its not there add it. Also check if module Newsletter is present in app/code/core/Mage.

Update 1

Check if \app\code\core\Mage\Newsletter\etc\adminhtml.xml is present and if it has some content. All problems that you described could happen if it is missed.

Update 2

Go to System > Configuration > ADVANCED > Advanced > Modules output and check if it is enabled.

Go to app/etc and find Mage_Newsletter.xml file. If it is not there open Mage_All.xml and find

<Mage_Newsletter>
    <active>true</active>
    <codePool>core</codePool>
    <depends>
        <Mage_Core/>
        <Mage_Customer/>
        <Mage_Eav/>
        <Mage_Widget/>
    </depends>
</Mage_Newsletter>

If its not there add it. Also check if module Newsletter is present in app/code/core/Mage.

Update 1

Check if \app\code\core\Mage\Newsletter\etc\adminhtml.xml is present and if it has some content. All problems that you described could happen if it is missed.

Update 2

Go to System > Configuration > ADVANCED > Advanced > Modules output and check if it is enabled.

Go to app/etc and find Mage_Newsletter.xml file. If it is not there open Mage_All.xml and find

<Mage_Newsletter>
    <active>true</active>
    <codePool>core</codePool>
    <depends>
        <Mage_Core/>
        <Mage_Customer/>
        <Mage_Eav/>
        <Mage_Widget/>
    </depends>
</Mage_Newsletter>

If its not there add it. Also check if module Newsletter is present in app/code/core/Mage.

Update Check if \app\code\core\Mage\Newsletter\etc\adminhtml.xml is present and if it has some content. All problems that you described could happen if it is missed.

Go to app/etc and find Mage_Newsletter.xml file. If it is not there open Mage_All.xml and find

<Mage_Newsletter>
    <active>true</active>
    <codePool>core</codePool>
    <depends>
        <Mage_Core/>
        <Mage_Customer/>
        <Mage_Eav/>
        <Mage_Widget/>
    </depends>
</Mage_Newsletter>

If its not there add it. Also check if module Newsletter is present in app/code/core/Mage.

Update 1

Check if \app\code\core\Mage\Newsletter\etc\adminhtml.xml is present and if it has some content. All problems that you described could happen if it is missed.

Update 2

Go to System > Configuration > ADVANCED > Advanced > Modules output and check if it is enabled.

Go to app/etc and find Mage_Newsletter.xml file. If it is not there open Mage_All.xml and find

<Mage_Newsletter>
    <active>true</active>
    <codePool>core</codePool>
    <depends>
        <Mage_Core/>
        <Mage_Customer/>
        <Mage_Eav/>
        <Mage_Widget/>
    </depends>
</Mage_Newsletter>

If its not there add it. Also check if module Newsletter is present in app/code/core/Mage.

Go to app/etc and find Mage_Newsletter.xml file. If it is not there open Mage_All.xml and find

<Mage_Newsletter>
    <active>true</active>
    <codePool>core</codePool>
    <depends>
        <Mage_Core/>
        <Mage_Customer/>
        <Mage_Eav/>
        <Mage_Widget/>
    </depends>
</Mage_Newsletter>

If its not there add it. Also check if module Newsletter is present in app/code/core/Mage.

Update Check if \app\code\core\Mage\Newsletter\etc\adminhtml.xml is present and if it has some content. All problems that you described could happen if it is missed.