Getting the NTP setup and running would be a great thing and good added knowledge.
I am pretty positive that I have tested running these EIGRP Auth labs and been able to get them running just by getting all of the routers timed at the same time. I have done it just by setting it up on my R1 router, copy the command I just put in and paste it into the others. It only put the routers off by a few seconds and then my neighborships formed after I changes the times on there.
Strange that it would not do it for you unless there are some of the interface commands being missed on some of the other routers. I believe some others have suggested to verify that as well.
Thank you Ahmed and everyone for mentioning that NTP needed to be setup on the routers. I struggled for 2 days beating my head against the wall on this issue. After reading this post, I configured NTP on my routers and EIGRP Authentication finally started working!!!
R1#show ip eigrp int detail
IP-EIGRP interfaces for process 10
Xmit Queue Mean Pacing Time Multicast Pending
Interface Peers Un/Reliable SRTT Un/Reliable Flow Timer Routes
Se0 1 0/0 56 10/380 640 0
Hello interval is 2 sec
Next xmit serial <none>
Un/reliable mcasts: 0/0 Un/reliable ucasts: 27/30
Mcast exceptions: 0 CR packets: 0 ACKs suppressed: 4
Retransmissions sent: 0 Out-of-sequence rcvd: 1
Authentication mode is md5, key-chain is "EIGRP_KEYS"