Why can't the valet key start the car?

What car ?

If the mystery car has keys with a micro-chip…
And, if through the life time of the car some new keys were made and programed…
AND if the valet key was not present at the time of programming additional keys…

The valet key got left out of the programming sequence so it now doesn’t work and needs programmed.

All cars come with 2 regular keys . A valet key is always key #3. It sounds like you only have 1 regular key. Where are the rest ?
If the family needed additional keys and forgot to program the valet at the time, that would explain it.

With my Fords you can program your own keys 3,4,5,& 6 but only if you have 2 that work.
With only one working key you must visit the dealer for programming of the 2nd.
All additional keys you make must be present during the programming sequence to work thereafter.
Even for family members in other towns who keep a key, Don’t forget them when making some more.