Primary domain controller has crashed, secondary does not log in
Solution 1:
Hrmmm.. I would suspect this is due to the global catalog and FSMO roles no longer being available. It SOUNDS like you just promoted a second DC without moving some of the other things over.
So some questions for you and I'll revise my answer as you respond:
1) Stop using the terms primary and secondary, these are deprecated and no longer applicable. It's a distributed directory system. Some machines are "in charge" of certain things but no one server is primary if designed right.
2) Is DNS resolving and responding to queries on the second server?
3) Are you absolutely certain the primary is not salvageable?
4) Do you have domain controllers at other sites perhaps?