If the PSU blew (as seems likely) - then they sometimes cause extensive damage to the system itself - and can kill the motherboard - which would prevent the system showing any sign of life at all.
Look on the motherboard to see if any LEDs light up - newer m/bs have them.
And see also of any fans are spinning, or try to.
Just check if there is a mains switch on the back of the new PSU - some have them!
Looks like real bad luck - did you get any sort of guarantee?