The problem was that I had a fresh installation of SQL2005 on a fresh box. I was migrating the existing DTS packages from a SQL 2000 box into SQL 2005 using the Legacy - Data Transformation Packages - migrate option. The packages appeared to migrate successfully, but I could not open them to view them! I had installed the SQL 2000 DTS Designer Components but was still receiving the following errors:
Sometimes, a similar problem can occur if you have dashes or underscores in DTS package names. It turns out this issue still occurs if you have spaces in you package names as well! So after simply removing the spaces in the package names, everything just worked!