Try booting up without battery in the compartment - use just the adaptor for power. If it works, reset the PRAM and PMU (power management unit) by unplugging the adaptor for a minute, then press the power button for 10 seconds. Replug the adaptor again, press power button and immediately press <commnad> <option> <P> <R> before the welcome chime is heard. I know it's hard, but an assistant to press the power button for you would be a real advantage. Maintain pressing on all 4 keys until you hear the chime, wait until another chime comes, then release. Power down, insert the battery and you should be good to go.
If this doesn't work, then it's a really bad logic board you're looking at.