Ok I had this happen to me twice in last year. Problem #1, Exact same thing was happening, All lights, fans, everything were on and no beeps or anything at start and no picture on screen. Solution #1, Tried everything including testing my PSU if it is putting out power and yes it was. Tried changing too much to remember before I put it in the shop. Was what I thought it was originally, the PSU. It was putting out power but no current. Was enough to power on lights and fans but would not power the major stuff. Just bought a new PSU and all was well (THIS PROBLEM HAPPENED TO ME TWICE WITH EXACT SAME SOLUTION)
Problem #2, Exact same thing again, lights fans everything worked with no beeps and nothing on screen. Solution #2, Tried PSU first(had one extra because of my problems in past) and nothing happened. It turned out to be my CPU. The pins were bent just very, very slightly when I installed it. I put it in the shop because I had no precision tools. Guy bent them back perfect and it posted just fine.
Those are my 2 exact problems and solutions, I am sure there is more but those are definetly something you should look into.
PS. If there is a problem with CPU it might or might not beep depending on problem.