ive never heard of a half working psu if it power up then its fine, a dead psu wouldnt power up at all , and in these sorta cases its nearly always the mobo , make sure the 4pin plug is connected to it
try resetting the cmos,do as follows
1) unplug the power cord
2) get the battery out for
1 hour then put it back (back exactly as it was and not upside down,in most mobos it should be with the + sign ontop)
3) plug the power cord & power up , if it posts then get into bios and load "optimized defaults" , save & exit
if it wont work then get all the ram sticks out and power up , if it doesnt beep then the mobo is defintly dead , if it does beep then put em back and get the video card out then power up and if it doesnt beep.. well its obvious , youll probably need to rma it
anyway after youll get it sorted , naturally youll have to buy an hd if you intend to use it