Maybe my brain is just running on fumes but I can't figure this out: It does the same whether I enter the model or serial number.
That is because it is a 70, not a 70C. Deere did not have a "C" in that model. They went from a 70 to a 70D. Below is a screen shot from out Parts Advisor.
This is what comes up when I enter the serial number:
Are you using a Deere App?
I tried the app and the website.
Many of the older Deere machines cannot be searched with a serial number. Just the model.