How is your CPU fan installed the wrong way, just the direction it blows in? it might affect your cooling, but it shouldn't stop it posting, you'd at least get a cpu fan or overheat error.
Just have a look at the headers on the motherboard and see if there is a speaker attached, if there isn't you get no beeps, you should get a single beep for a successful post on most asus boards. Other than that there are several beep codes you can google.
Pulling components is always a pain, I'd start with ram, try a single stick in each ram socket, then try another stick in each socket if you have no luck. disconnect the hard drives/dvd as you can worry about that once you get it to post, and you want bare minimum plugged into your PSU, as it could be failing.
You could do with a spare graphics card, as you're not getting any output, but since you don't have one , you may as well start here.
You could also try resetting the bios/cmos, this is from the Asus Forum;
Clear CMOS (RTC RAM):
* Remove the CMOS battery.
* Move the jumper cap from pins 1-2 (default) to pins 2-3. Keep the cap on
pins 2-3 for about 5~10 seconds, then move the cap back to pins 1-2.
* Reinstall CMOS battery.
* Plug in the PSU power cord and turn ON the computer.
Without spare parts you're pretty limited in what you can do.
And really check the monitor cable/pins, because you'll kick yourself if it's that.