if it does not do it's "post beep" could be a funky connection on the CPU. if you pull off that cooler and pop out the CPU and stick it back in again, it may start working again.
i have encountered some motherboards if they have been reset to default (dead bios battery or the like) will not boot up without a good voltage reading on the battery and the "first" video device being connected...
typically this is the lowest connector on the totem pole. (typically this goes VGA, then HDMI/DVI, then display port) so unfortunately if you have a VGA port on the board, you may have to find a VGA monitor just to see if things are booting.
failing that, iv'e had limited success erasing the CMOS settings (a jumper setting or remove battery, you'll have to check your particular board.)