> Can anyone suggest the simplest connection of PIC16F628A?

The simplest is that it has just power. Use the internal oscillator
and disable MCLR

> Target Device ID (00000000) does not match expected DeviceID (00001120).

Are you connecting to the correct pins for programming ? Double
check. How you have the 628 configured for run-time shouldn't
affect the programmer (as long as any circuitry isn't interfering with
the programming)

> so I am not sure if the PIC is faulty

Unlikely, but not impossible of course

> or the schematic is  faulty

Hmmmm

> Is 3.6V as power supply enough?

Yes. Vdd is 3V - 5.5V
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