https://www.amazon.in/dp/B0102ESMW6/ref=cm_sw_r_u_apa_i_RP2Q39R6EQ0KDDTC1RWA
I don't know what's the actual age of PSU I literally Don't have any idea of its age as it's a second hand pc
In order to rule out any possible problem with the case power button or its cable you can try powering on the system with the power on (might be marked as PWR_ON on board) pins on the motherboard. You can gently short the 2 pins with something metal, tip of a screwdriver for example. You didn't provide your motherboard model. Check with its manual on ASRock webite for the board to fid the power on pins.
If the system starts there might be something wrong with the case power button or the cable connecting it to the pins on the motherboard.
I don't think that's a good quality PSU and it wasn't a good one even when it was brand new. You say it was used/second hand and you're not sure about it's age. For all we know the previous owner might have even repaired at some times and sold it.
That Amazon page doesn't even have real specifications as in how much power it can/could deliver on 3.3 5 and 12 volt rails. I couldn't find real specs via search either.
The PSU might have failed or is failing. I think easiest way is to try to power system with another known wokring PSU.