Vostro 420 does not boot

first thing to do in this old pc is to replace cmos battery (aka coin cell battery) with a brand new one.  refer to p.117

Dell Vostro 420 Service Manual

If still does not POST, then try clear cmos settings.

Clearing Cmos Settings - Dell Vostro 420 Service Manual [Page 135] | ManualsLib

then it is possible either the motherboard or psu has failed.  if you have a spare 24/4 pin atx psu that works in another pc, borrow it to test the 420 motherboard.  you only need to disconnect the 24 and 4 pin connector of stock psu from mobo and connect the test psu.  if pc boots, it proves the old psu is not good.  if a good test psu still cannot boot the mobo, it seems mobo is gone.  based on what you said that the power button is blue, but no beep when power button is pressed, it is more likely that mobo has died.  Of course, make sure your video cable is not loose and your monitor is still working.

another test you might try do is to remove all memory sticks.  then power on 420.  if pc beeps when no memory present, it is some good sign that mobo is not completely dead.  If no beep at all, not good sign of mobo.

I did the above two steps (the coin battery changed and Clear CMOS settings), but the issue is still there.