If the New Comment button is missing for some users, there are two likely possibilities:
1. The user's profile has a different case page layout assigned to it. To check this, first determine the affected user's profile by going to Setup > Manage Users > Users and click on the user. Next, navigate to Setup > Customize > Cases > Page Layouts. Click on the Page Layout Assignment button at the top and match up the Profile (and Record Type if applicable in your Org) with the assigned Page Layout. Click on the Page Layout and verify the button is in fact present in the Custom Buttons area.
2. The user does not have a license assigned to them. Navigate to Setup > View Install Packages and click Manage Licenses next to Email to Case Premium. Ensure that the affected user is listed under the Licensed Users column. For additional assistance, click Help for this Page in the upper right or contact firstname.lastname@example.org for further assistance. Note that if you do not have an option to Manage Licenses, you have a site license and this step is not applicable to your organization.