How do I know what's wrong with my PC?

I was having problems with my computer shutting down on its own and then I wasn't noticing a fan running prior to the issues. One day I came to the computer and nothing would turn on. I also noticed that the outlet had been tripped because other things plugged into the surge protector were reset. I purchased a power supply and replaced it but nothing is turning on. What other suggestions do you have to see what is the matter? I would like to at least get the information I have stored off of the computer, so any ideas on how to do that would be helpful too.