How to determine whether computer is on Domain from event logs?

I'd recommend you check the Security section of the Event Viewer (or the appropriate log):

If you open an entry here, you'll see a log entry for some authentication event. The event I opened here was validated against the domain WINXP. That is, in fact, the name of the workstation, not a domain controller:

So this could be a hint that the whole machine is not connected to a domain. If you check more entries, you can see if there ever was an authentication event against another machine (maybe a domain controller).

I don't think this would be a reliable way to determine if a client is, in fact, a domain client. But it might help.

Just FYI, a quick way to determine if the machine is part of a domain if you have access to it could be to:

echo %LOGONSERVER%

on a command prompt. If it prints the local machine name, it's not part of a domain. Otherwise, it should print the name of the domain controller.

Just do a search for 3260 this is the event that will show in the system log when a PC joins a domain.

Event 3260