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7400 TTL needs more current to pull the input low than you'll get through the 10K resistor. Even if the output could go all the way to ground, getting the input down to .4V with as much as 1.6mA would require the resistor to be as low as 250 ohms. Then you may need to increase the size of the capacitor a lot to get any oscillation at all. Since TTL inputs are referenced to ground, it would be better to take the capacitor to ground instead of Vcc. Although they're supposedly the same thing for AC signals, they won't be in practice.
The circuit should oscillate if you replaced the 7404 with 74HC04, but you would not get a square wave out of it, and you may not have very good control of the frequency. To get the square wave, use an inverter with hysteresis, like the 74HC14. Frequency will still depend on how much capacitance you have from the input to ground (remember there are a few pF inside the IC, and you'll have stray capacitances on your circuit board), as well as on temperature, operating voltage, and the particular IC's production lot (because of variations in the amount of hysteresis).
I don't have a bench signal generator that can output a square wave in the multi-MHz range; so when I wanted to see how fast my workbench computer would run, I breadboarded a little square-wave generator with the same basic configuration you have above. Instead of a 10K resistor, I put in a 50K trimmer so I had fine control of the frequency and could vary it while it's running. Instead of just your 10pF capacitor, I put in a 4.7pF to ground, plus in parallel with it on DIP switches, a 10pF, 22pF, 47pF, 100pF, 220pF, 470pF, and .001uF. The DIP switches gave me overlapping ranges, leaving the trimmer for the fine adjust. Then I followed the 74HC14 inverter with the others in the same package for more output drive current. The first inverter's output (pin 2) went to the inputs of all the other inverters. Their outputs were all connected together, and fed the oscilloscope or frequency counter as well as the workbench computer I was testing for speed. If I pull that breadboard back out to use it again, I'll replace the 74HC14 with a 74AC14 since AC has much faster propagation and rise and fall times.
_________________ http://WilsonMinesCo.com/ lots of 6502 resources
The "second front page" is http://wilsonminesco.com/links.html .
What's an additional VIA among friends, anyhow?
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