When I was in this situation most recently it had to do with the seating of the memory SIMMS (or DIMMS, or whatever they're calling them nowadays). Screen would not come on, nothing. Maybe even the clicking, don't remember. What you do is make certain they are making contact and are firmly seated in the sockets. Possibly clean them with a 91% alcohol-dabbed Q-Tip (wait a few minutes for alcohol to evaporate if you do this.). Ensure the notch on the bottom edge matches up with the little hump in the socket seating.
A quick note on processors, fwiw: replacing the processor is a pain, as today's processors are so electrically inefficient you could practically heat a small room with them; make DARNED SURE you've got that heatsink fully contacting the CPU, and preferably with a dab of silicon grease between them. One split second without a heatsink is sufficient to fry it.
This is just from my experience. I defer to the experts of course, but want to emphasize djf's point: minimize the potential points of failure and take baby steps.
I've had the same problem with SIMMs. Best once you get them seated and working, never mess with them again.
BTW, you know what I use for the heat sinks? Gives great contact and has never failed on me. Solid at room temp but melts quickly.
Vaseline.