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I am sorry to hear about this microchip not working. I am sure this was checked: is the correct microchip reader being used for the type of chip he has? Sometimes chips migrate; was his whole body checked for the chip, not just the back of the neck?
You should be OK on rabies; you should have a rabies certificate and proof of rabies in his passport. If you do not, you can always get another vaccination. Also, you are coming from a rabies free country (UK) so you may not need proof of rabies. His microchip is not proof of rabies vaccination, his rabies certificate is. If you have a document proving he had a rabies vaccination in the last 3 years, you should be able to enter the US.
Here is a webpage about US regulations:
You might want to get another microchip implanted if the one he has is truly not working.
Let me know if this helps, and what else I can answer.
I did not hear back from you; I hope you were able to see what I wrote! Let me know if I can help with or answer anything else.