If I got a used computer (cracked OS or not) I would just reinstall Windows from scratch - a clean install.
Who knows what else on the system is cracked, broken, afflicted, nefarious, etc. and if you do a clean install you will not be spending future time attempting to fix other problems that might come up.
With a little more more information the "expert" from Microsoft should be able to help.
Exactly what does "I haven't been able to install any updates" mean? You don't see updates, updates don't download, updates download but don't install, something else you will describe?
Exactly where are the "options to activate Windows missing"?
Do you not see this on the Control Panel, System page:
What is the system make and model or is it assembled from components?
If a Dell what is the Service Tag number?
If an HP what is the serial number?
What Edition (Home, Pro ,etc.) is for your legit license key and it for Home Premium?
I'm sure the "expert" from Microsoft will be able to help with this situation.