First conform there is power to the socket (plug in a table lamp or something to check).
If YES, then something on the PC has died but it could be just the ON/OFF switch ;-)
If you are able, open the PC case and with the it connected to the mains, short the ON/OFF switch temporarily with some insulated long nose pliers or the like. (don't worry - small voltage here).
If nothing happens then start looking at the PSU.
Just try to find a replacement to the one you have then it's one out/one in with no complications.