I had a similar infinite reboot cycle after my son downloaded and installed Protemac logonkey. He misunderstood what it did, but that became irrelevant because the iMac failed to reboot from that point on.
The apple log would appear, then the spinner would cycle for a few minutes before freezing.
To fix, I tried rebooting in safe mode, verbose, single user etc but it made no difference. The safe mode verbose logging would echo the actions being taken, but at a point in the process the screen would clear to plain black, with just a single white cursor square in the top left hand corner of the screen.
Rebooting into recovery mode, and using terminal (thank goodness for that), I removed the .app bundle, and some cache files (/Library/LaunchAgents etc) and preferences using rm Library/Preferences/com.apple.security.plist, but no joy. I also did all the available disk checks, and a few (irrelevant) errors got fixed.
Looking at the logs it looked like some kind of authentication failure, most probably to do with the logonkey installation. After many hours trying to find out how to uninstall the offending plugins, trying just to "unplug" the authentication itself, then wondering if it would end in salvaging what I could from the hard drive, wiping the disk and perhaps an expensive Genius bar visit, I came upon this post. And this worked (as per above):
1) Boot into single user mode (CMD-S while rebooting)
2) Mount the harddrive, type "/sbin/mount -uw /"
3) Type "rm /var/db/auth.db"
4) type "reboot"
Never has a set of four commands been so much of a relief!
I am posting my logonkey specific logs here in case anyone else gets the same problem, or similar. iMac running version OSX 10.9.5.
In /Volumes/Macintosh HD/private/var/log/system.log :
Nov 22 10:13:55 the-imac.home UserEventAgent[325]: Failed to copy info dictionary for bundle /System/Library/UserEventPlugins/alfUIplugin.plugin
Nov 22 10:13:55 the-imac.home com.apple.authd[71]: engine[321]: evaluate returned -60008 returning errAuthorizationInternal
Nov 22 10:13:55 the-imac.home loginwindow[321]: Login Window - Returned from Security Agent
Nov 22 10:13:55 the-imac com.apple.launchd[1] (com.apple.security.agentMain.00000000-0000-0000-0000-0000000186B4[331]): Job appears to have crashed: Trace/BPT trap: 5
Nov 22 10:13:55 the-imac.home loginwindow[321]: ERROR | -[LoginApp performAuthPluginRequest:] | AuthorizationRef doesn't have a username. Exiting.
Nov 22 10:13:55 the-imac.home WindowServer[322]: CGXRestartSessionWorkspace: session workspace exited for session 256 (on console)
Thread dump
Thread 0 Crashed:: Dispatch queue: com.apple.main-thread
0 com.apple.CoreFoundation 0x000000010392f4c4 CFRelease + 724
1 com.apple.securityAgentPlugin.NameAndPassword0x000000010cbf595e TrialProtector::getInstallDate(guid_t) const + 94
2 com.apple.securityAgentPlugin.NameAndPassword0x000000010cbf5c49 TrialProtector::trialDaysLeft(int) const + 85
3 com.apple.securityAgentPlugin.NameAndPassword0x000000010cbf4b86 -[LogonProtector daysToTrialEnded] + 335
4 com.apple.securityAgentPlugin.NameAndPassword0x000000010cbf3163 -[EXNameAndPassword awakeFromNib] + 381
5 com.apple.AppKit 0x0000000102623b3f -[NSIBObjectData nibInstantiateWithOwner:topLevelObjects:] + 1223
6 com.apple.AppKit 0x00000001026185ce loadNib + 327
7 com.apple.AppKit 0x0000000102617b6c +[NSBundle(NSNibLoading) _loadNibFile:nameTable:withZone:ownerBundle:] + 288
8 com.apple.AppKit 0x0000000102bf0f87 -[NSBundle(NSNibLoading) loadNibFile:externalNameTable:withZone:] + 150
9 com.apple.securityinterface 0x0000000101df77e4 -[SFAuthorizationPluginView initWithCallbacks:andEngineRef:] + 341
10 com.apple.securityAgentPlugin.NameAndPassword0x000000010cbf2eac -[EXNameAndPassword initWithCallbacks:andEngineRef:] + 105
11 com.apple.securityAgentPlugin.NameAndPassword0x000000010cbf0de7 -[EXAuthPluginMechanism invoke] + 205
12 com.apple.securityAgentPlugin.NameAndPassword0x000000010cbefe65 MechanismInvoke + 41
13 com.apple.SecurityAgent 0x0000000101912a21 0x10190f000 + 14881