You're making a huge leap from version 3.1 to 6.2, so you can expect some header files to change.
Try this:
1) Create a new project in v6.2 using the New Project wizard, and choose your target MCU. The new project you make can be one of the demo programs. Don't use your source code.
2) Confirm that CodeWarrior builds the demo project successfully and downloads it to the target.
3) Right-click in the CodeWarrior Project window on each source file that's part of the demo and remove it from the project. Leave the startup files alone.
4) Place copies of your source files into a folder named MySource. Drag this folder into the CodeWarrior Project window, and when prompted, add them to the project.
5) Pick Project > Remove Object Code, then Project > Reset Project Entry Paths. Try building this project again.
What you're doing here is adding your source files to a project that's proven to work. This should keep the errors that appear to a manageable level. There might be errors, but hopefully only with regards to missing or modified header files. You should be able to compare the header files between the old project and this new one to determine what's missing or moved.
---Tom