I am unable to write anything in the body of a new message on Outlook Web Access and it shows as a broken image (red cross). I am also unable to reply to any existing message or create any other new item.
Is this something I need to fix in Internet Explorer or is this issue on the server?
This is caused by an incompatibility between Exchange 2003 and later Internet Explorer updates (ActiveX Activation Patch).
Contact your mail admin and ask him/her to apply the OWA/IE compatibility update KB911829 to the Exchange server.
Updating Exchange 2003 fixes OWA again after applying the Internet Explorer ActiveX Activation Patch.