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Tutorial:
1. Step:
Start Battlefield 2 without changing anything.

2. Step:
Start the CD-Key Changer, type in your CD-Key and press Apply.
You have to run the tool as administrator!

If you don't want to use the CD-Key Changer, here the *.reg files:
Windows - 32Bit
Windows - 64Bit

3. Step:
Delete or rename this file:
C:/Program Files/Steam/steamapps/common/battlefield 2/installscript.vdf

4. Step:
Run Battlefield 2 as Administrator.

5. Step:
Try out if it works. If you still get the error, go back to Step 2 and tick the "Don't include hyphens" checkbox before pressing Apply.

If it works:
Enjoy Battlefield

Screenshots: