TTL logic ring oscillator
I am assuming that you do not have an oscilloscope, and are looking for visible indicators of oscillation. If I'm wrong, you can ignore the following.

The answer is (I suspect) pretty simple: in both cases there was nothing wrong with the circuit and it was working just fine.

Of course, with the RC values you've got (1 kohm/1 uF) I'd expect an oscillation frequency in excess of 30 Hz, so the LED in the second circuit would appear to be on steadily. 

The test for this is to measure the capacitor values again, but this time with the meter set to AC rather than DC. If the circuit is really not oscillating, the meter will show 0 volts, or pretty close. If it shows about 2 volts, you know it's working. Alternatively, for the second circuit, observe the LED brightness. Now disconnect the input of the Schmitt trigger from Vout and ground it. If the LED brightness increases, you know that the LED drive was not on 100% of the time, and the circuit was oscillating.

Also, for what it's worth, for relatively low oscillator frequencies all of the gates should be Schmitt triggers, such as a 74(HC)14. Logic gates have been known to do Bad Things when their inputs vary slowly.