well first off, what type of motherboard/cpu/ram ect.
second that PSU is old and it would be best to replace it...
what do you mean LED's pluged in correctly?
does the green LED on the system board come on?
the #1 killer of a cpu is when putting it in and taking it out... are you sure something didn't happen, were you properly grounded when handleing the cpu?
ESD (electro-static discharge) can kill a cpu fast. kinda like when you rub your socks on the carpet and shock someone... only the amount required to kill most electrical components in a computer is so much less than that charge that you can't even feel it. that's why it is always a good idea to get a wrist band that grounds you to the case you are working on... available most anywhere computers or computer parts are sold.
given that, as you say, nothing happens i am willing to bet it's the PSU.
here is a link so you can see what kind of wristband i'm talking about