I'm running TeamCity 6.5.3 and for many release now I've been having this problem: Build configs whose "Time to start" are marked as Never: Can run on No agent.
This has always been annoying, but the build would be run anyway, so I figured this was most probably a known bug that you were working on. I was hoping that 6.5.3 would fix this, but it didn't.
I have configured one of the problematic build to run on a different agent, and since then the build has not ran a single time as it is stuck in the build queue. Now the "Never" Time to start is right: it never starts. I have cleaned the whole build queue a couple of times, tried to force it to run, to no avail.
I have reconfigured it to run on the previous agent and it seems ok. It is still telling me it will Never be run, but there is a "Can run on 1 agent" at least. I don't know why this is any different than the previously assigned agent. That one was reported as compatible all right too, no conflict in the requirements, I don't get it.
I don't know what causes this and would very much like it to be fixed. I am considering downgrading the version of TeamCity until I found one where this seems to work, but the annoying first part has been there for so long, that I don't remember when we first noticed it.