Lincoln LS

I own a 2006 LS and I could not get inspection done because the said diagnostic plug on car was not working but there is no engine light on.

If the diagnostic port is not working, then you will have to get it fixed before you can pass inspection. Are you sure that they were using a CAN compatible scan tool?

The test port has a 12V power feed. Ford likes to fuse the power to the test port either through a dedicated fuse or the fuse that protects the cigarette lighter/ accessory port. Check the fuses. It fixed my problem last time I had this exact same problem.