Removing dead Exchagne 2003 servers from the Exchange System Manager and Active Directory please follow below mentioned steps

1. Open Exchange system Manager
2. Expand Adminstrative group until you reach the required server
3. Right click on the server -> All Tasks -> Remove Server
4. Confirm the same by clicking yes.

If this did not help then you may need to Dig into Active directory through Adsiedit and remove the server Manually

Go to Start, Run and write ADSIEdit.msc and hit OK button.

Configuration Container
CN=Configuration, DC=Domainname,DC=com
CN=Services
CN=Microsoft Exchange
CN=Your_Organization_Name
CN=Administrative Groups
CN=AdminstrativeGroup_Name
CN=Servers
Right click on the Required server click Delete  and confirm the same.