Class D Amplifier is not working?
Although there are some problems seeing images in the question at the moment, the fundamental problem you describe seems to be just with the behaviour of the 74HC04.
Therefore you should temporarily troubleshoot just that part of the circuit. Don't complicate your troubleshooting (and this question) with other parts like the 555 timer and MOSFET driver. Disconnect those parts and just troubleshoot the inverter.
There is already one big problem in your description so far. You said:

In the schematic shown, in the hex inverter rest of pin is not connected with the ground, but in reality, I have grounded every pin except 1,2,14.

Don't do that! You must not connect unused outputs of the inverters to Gnd. That risks causing excessive current in the inverters and possible damage. Only unused inputs should be fixed at a valid logic level. Unused outputs should be left unconnected.
You might have damaged the 74HC04 devices where you made those incorrect connections. In any case, as I said, you need to focus on checking the behaviour of the inverters (or at least the one inverter you are using in that package) separately from the other parts of your design.

To answer your newly added question:

Is there any difference between MC74HC04A and SN74HC04?

No significant difference in behaviour, provided you stay within normal operational parameters. They are just made by different manufacturers.