As it was said above, there are more than one key. It is likely that there is a confusion between those, so let me elaborate a bit:
- On the first step (the “Details” screen) the key is the LE account one.
- On the last step, if you had CSR generated for you on the “Details” screen, there will be a certificate and a domain key to use with that certificate - this is what you need to use while installing/importing the certificate on your server.
Now it is important to remember that if you are using the CSR made earlier or created by other means, the “Certificate” screen will only show the certificate itself but not the domain key, because this is what you have already from earlier or from your own process of CSR generation.
If you have not downloaded the domain key on the last step or if you misplaced it, the easiest way to recover from this is to redo the process using the same LE key as you used originally but let new CSR to be generated. Since you have verified the domain already, you will be taken straight to the “Certificate” screen with both the certificate and the domain key (please note that it will be updated certificate, so download it too).
I hope that helps.