Just because no signal goes to your monitor doesn't mean it's a video problem like most people are prone to jump to.
You need to put the motherboard on wood, glass, antistatic bag, cardboard, something that won't short it...make sure your case is nearby so you can hook up the PC speaker.
Plug in just one stick of RAM, vid card, and keyboard then see if you get any response.
Pull out the video card, if it beeps, chances are the video card is at fault here and preventing the system from POST'ing.
If no beeps, put the vid card back in, and remove the stick of RAM, same thing, if it beeps, chances are it's the RAM...if still no beeps, then as a last ditch effort, trying pulling out both the RAM and the vid card, if the board still does not beep then the CPU or motherboard is at fault here.
The bios battery shouldnt prevent a signal being sent to the moniter though surely.
With no battery, the CMOS isn't holding any information, which means it can't even access the BIOS, therefore, it has no instructions to even POST, hence no working computer